## Wednesday, August 15, 2018

### [mwnxlwvg] Diamond chess

Create a variation of chess that uses only one color of squares of the checkerboard, like checkers.  Create a variation of chess that not only uses all the squares of both colors, but also pieces can be placed on vertices where 4 squares meet.

These problems are actually identical at different sizes: a diamond-shaped board.

## Tuesday, August 14, 2018

### [xrwrxqye] Logarithm arc length

The arc length of logarithm base B has closed form: InputForm[Integrate[Sqrt[1 + 1/(x^2*Log[B]^2)],x]] = (x*Sqrt[1 + 1/(x^2*Log[B]^2)]*(Sqrt[1 + x^2*Log[B]^2] + Log[x] - Log[1 + Sqrt[1 + x^2*Log[B]^2]]))/Sqrt[1 + x^2*Log[B]^2]

arc length common logarithm from 1 to 10 = 9.0834719397922

arc length natural log from 1 to e = 1 - sqrt(2) + sqrt(1 + e^2) + log(1 + sqrt(2)) - log(1 + sqrt(1 + e^2)) = 2.00349711162735247857

arc length log base 2 from 1 to 2 = 1.42116

(via Wolfram Alpha and Mathematica)

Previously, on why we might be interested in the arc length.  It turns out arc length is dominated by movement in the x direction, so it is probably not the right measure to use.

## Monday, August 13, 2018

### [byhnlnng] Commonly occurring substrings in pi

We calculate the most frequently occurring N-digit sequences in the first 10^N digits of pi past the decimal point.

N=1: The most frequently occurring single digit in the first 10^1=10 digits of pi past the decimal point is 5.  It occurs 3 times: 1415926535.

N=2: The most frequently occurring 2-digit sequence in the first 10^2=100 digits of pi past the decimal point is 62.  It occurs 4 times: 1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679.

Below is a table extended up to 10-digit sequences in the first 10^10 digits of pi.  When there are ties, all sequences are listed.

(N, number of occurrences, [the N-digit sequences that occur most frequently])
(1,3,[5])
(2,4,[62])
(3,5,[019,105,171,446,609])
(4,6,[2019,2916,7669])
(5,8,[17663,91465])
(6,9,[919441])
(7,9,[0123880,1296878,2009579,2399789,2572735,3707493,4515163,4900343,5707393,8730991,9219118,9435538])
(8,11,[12058610,77114204])
(9,12,[550527601])
(10,12,[2063323454,2612299524,2907884134,4880022211,5078602578,5421790974,7646964010,7711937174,8193684176,9522257435,9725290655])

We stopped at N=10 because, for a computation involving pi in base 10, stopping at 10^10 digits seemed appropriate.

It is curious that the middle column, number of occurrences, is non-decreasing.  We don't expect this trend to always be true.

Assuming the digits of pi are random, we expect a typical N-digit sequence to occur once in 10^N digits.  This isn't exactly correct because digit sequences overlap so are not independent.  I don't know the probability distribution of the number of occurrences of the most common sequence.

Here is Haskell code used in the computation.  We used strict state threads (Control.Monad.ST) to avoid lazy thunks from piling up, a frequent occurrence in long computationally intensive tasks which produce output only at the end.  We used `seq` to get rid of one giant space leak at the end when finding the largest item (and its index) of the array discussed below.

We used the unboxed `STUArray s Integer Word8` to compactly store the counts for each possible digit string.  We furthermore packed 2 entries into each Word8, one in the upper 4 bits and one in the lower, at the cost of limiting maximum counts to 15 (which turned out to be enough: the maximum seen was 12).  For N=10, we were therefore expecting 5 GB memory usage for the 10^10 digit run, but memory use was 9848268k maxresident (9.8 GB) according to /usr/bin/time, so there is still a space leak somewhere.  CPU time was 6000 seconds.

## Wednesday, August 08, 2018

### [hrjjayzd] Bracketing delimiters of different heights and positions

Upper parentheses (as implemented by quotation marks), centered parentheses, etc.

Having different brackets is sometimes useful.  Height and location relative to baseline is useful for visually distinguishing them.

German has a low start quotation mark.  French guillemets are not full height.

### [okfcvwxz] Subsidizing gun security

If the state wants to prevent unauthorized people from using someone else's weapon to hurt themselves or others, then the state should subsidize gun locks, safes, etc.  People having effectively more money to buy such safety goods will induce competition among producers to produce good products.  This is in contrast to regulations (e.g., Maryland) forcing people to purchase a gun lock with a gun, resulting in competition among producers to produce the cheapest possible joke of a product that barely qualifies as a gun lock.

Of course, the devilish detail is, where should the money to pay for the subsidy come from?  Logically, it should be taxes on the general population, those whose safety is increased by gun owners securing the guns better.

Having a legal set up that permits third-party gun storage in a way that is immune from being confiscated by the state would also increase safety by decreasing unauthorized use, but it seems states would rather keep their power to confiscate -- eliminating that type of business -- even if it means more people get shot.

## Monday, August 06, 2018

### [irjqykvh] Bribing the police for great justice

In a regime in which the police are corrupt, bribable, the police will naturally target the rich to maximize their revenue from bribes.  This logic probably applies to the rest of the justice system also.

Therefore, measures to decrease and limit corruption in the justice system are to protect the rich.  These measures were put in place using the political power of the rich.  If you have politically supported an honest police force, did you realize this is what you were supporting?

A justice system that targets the rich will somewhat correct for the tendency of the rich use their wealth to get richer, perhaps through buying privacy or expensive lawyers to thwart becoming convicted of crimes.

If the justice system disproportionately targets the rich, more poor people will get away with crimes, especially crimes in which the poor steal from the rich.  This another income redistribution mechanism in the style of Robin Hood.  Unfortunately, there will also be more instances of the poor committing crimes against each other, then the police not caring.

What else goes wrong?

The police might not target the rich if the sum of expected profit from bribes from many poor people would exceed the sum of bribes from the fewer number of rich people.  Targeting does require investigative effort, a cost outlay: if you look at anyone closely enough, you will find some crime they have committed, but you do have to look at them closely enough, and that takes effort, a cost to be figured into expected profit from bribes.

Instead of bribes, can we induce incentive to maximize revenue from fines?  Essentially the same system as bribes but made explicit.  We probably want a system in which one goes to prison only if one cannot pay the fine.  The conventional view of the guilty rich buying their freedom is resentment, but it should be the opposite: assuming the state is going after the fine revenues from the rich, it's good to be poor.

### [hnhczjsg] Accelerate the sun with solar power

Assuming one can harness the entirety of the sun's power to move the sun (e.g., Shkadov thruster), how long would it take to accelerate the sun to, say, half the speed of light?

This should be easy to calculate.

## Sunday, August 05, 2018

### [znelkrxv] Nice path through points

Draw a path of line segments connecting 10 out of 12 points of a 3x4 lattice such that the path does not cross the same lattice point more than once.  The 10 points represent digits in scrambled order, and the path aids finding digits.

The path may not intersect itself on any of the 10 selected lattice points nor coincide with another segment of the path.  The path may intersect itself not on a lattice point, or on one of the 2 unselected lattice points.  How many possible paths are there?

Previously (1), (2).

## Saturday, August 04, 2018

### [fqdvjfsb] Social lab animals

Understanding human society is stymied by the expense and difficulty, often impossibility, of controlled experiments.  However, there are a good number of social lab animals to experiment on.

Maybe understanding of a lab animal's society doesn't directly translate to human society, but it still seems an interesting subject to study in its own right.

Inspired by the question: when do a bunch of social animals get along?  When do they not?  There's likely plenty of complexity suitable for groundbreaking research.  I don't feel we have a full understanding of even, say, rat social behavior yet.

Inspired by Rat Park.

### [bzwxhzvm] Same story different tropes

Tell a story multiple times, each time relying on tropes from different cultures/subcultures as scaffolding to build the story.  Of course, this is difficult, needing to be versed in tropes of multiple cultures.

This is in response to those who protest a story for the tropes it employs, often identity politics.  Protesting scaffolding misses the point of the building.

A good story captures something universal about the human condition, so should be translatable.

Ambitiously, create a tool to translate a story from one culture's tropes to another's.

### [dlvfdfoa] 3 space colonization targets

Moon, Mars, more space stations.

Moon: closer than Mars, easier to travel to and fro, more solar power.  Mars: (probably) more water, more gravity, atmosphere shield against radiation and meteorites.

Space stations: even easier travel.  If we are to become a K2 civilization, we need to practice building space stations.  Prefer to leave Moon and Mars uninhabited because we may eventually disassemble them for raw materials to make many space stations.

We have yet to build a space station with a radiation shield that reduces space radiation down to levels seen at the surface of the earth.  Also yet to build one with artificial gravity (via centrifuge) equal to earth.  We'll want both to prevent human evolution from diverging relative to earth.

## Friday, August 03, 2018

### [qtomlpcn] More color-bound chess

A chess variant in which more pieces are colorbound:

Rook instead moves like a dabbabarider + ferz compound.

Queen = dabbabarider + bishop

Knight = camel, or camel + alfil because camel is pretty weak.

All other pieces remain the same.

If only 1 queen per side, then we want some way for it to be able to change parity (color).  Easiest is to also add a wazir ability.

Maybe being adjacent to a king causes a dabbaba piece to temporarily gain the ability to move like a king, namely gaining the wazir move.

Or, drops like bughouse, shogi, crazyhouse.  This was vaguely inspired by considering a chess board as two separate boards (like bughouse) of different parities which are only weakly interacting.  Pawns, not colorbound, become even more intensely the soul of chess.

Or, start with 2 colorbound queens, one of each color, per side.  Adding one more non-colorbound piece, perhaps orthodox knight or Man, would give 10 pieces for a 10-wide board, and the larger board is nicer anyway for camel.  Or 2 kings per side: capture either, or both?

Move up to two pieces, one per parity, on each turn?  This might counterbalance how the 10x10 board is less dense so leads to fewer fights.  A parity change move (king, pawn, Man) can be accompanied by a second parity change move in the opposite direction.

Or, get rid of queen, replace with Man.  Colorbound queens can appear at pawn promotion, requiring strategy to pick which parity square the pawn promotes on.

### [joprgfhe] Shor's algorithm not working

We boldly hypothesize that if we build a sufficiently large quantum computer and try to factor a large integer with it, we will find it doesn't work due to a previously unknown fundamental physical limitation of the universe.  Therefore, we should put LHC levels of effort (and funding) toward quantum computing to probe the deepest secrets of the universe.  (This may already be happening for other reasons, commercial intererst in quantum computing.)

The intuition is that Shor's algorithm seems too good to be true.  Maybe we're living in a simulation, and large quantum computers are annoying to simulate so the universe is designed to make them not possible.

Take some famous songs with good endings and replace their original endings with a fade out.  This might require some composing and re-recording.

Try this on classical songs, which never fade out as originally written, because the technology didn't exist.

The point is to highlight how infuriating a fade-out sometimes is.

### [pwtykzsq] Anakin defeats the younglings, barely

One of the greatest scenes omitted in Star Wars is Anakin killing the younglings in the Jedi Temple.  (Of course, political correctness prevents even considering shooting that scene.)

Tell a story that that battle was not so easy for the new Darth Vader.  We introduce the following mechanic to make it interesting:

The main thing Jedi Academy teaches these days is not how to increase one's strength in the Force, but how to avoid the Dark Side of the Force.  The younglings have not mastered how to do this yet: therefore, in the battle against Anakin, they somewhat freely use Dark Side techniques (not yet knowing better) against Anakin, also because anything goes when you are fighting for your life.  They are not very good at those techniques, nor at Light Side techniques, but there are a lot -- hundreds? thousands? -- of younglings.  Vader has to deal with waves and waves of raw yet-to-be-tamed offensive and defensive Force aimed at him by the younglings.  This rawness is a side of the Force we have yet to see.  The kids fight viciously, they fight dirty, they flight like a pack of Force-wielding small wild animals.

Some Stooges comedy: poorly aimed Force chokes occasionally pinch his nose or jab him in the eye.

## Wednesday, August 01, 2018

### [zikyrfrx] Morse-like code organized phonetically

We present a code similar to Morse code but the letters assigned to codes phonetically for easier learning.  Vowels proceed front to back, then consonants very roughly front to back.  Unvoiced consonants (ending with zero) are immediately followed by their voiced versions (ending in one).

Builds on previous.

i 0
e 1
a 00
o 01
u 10
(unassigned) 11
p 000
b 001
m 010
n 011
f 100
v 101
t 110
d 111
s 0000
z 0001
l 0010
r 0011
c 0100
j 0101
k 0110
g 0111
h 1000
w 1001
q 1010
x 1011
y 1100

Several things could go to the unassigned code 11: y r n, as these are common letters that don't really match with their phonetic pair that well. But leaving it unassigned as an escape code is probably best.

### [gzzhbeha] Tribalism as norm

A pessimistic outlook on human history: we always revert to tribalism as the norm, unless some unusual and ephemeral circumstances (e.g., sudden access to a large quantity of natural resources) allow us to temporarily "get our shit together" on a larger scale than tribes.  The large nations we currently see are an aberration.

Maybe not tribes of population up to 100 but slightly larger city-states?

Counterarguments: technology has increased speed and lowered costs of transportation and communication.  Nuclear weapons have increased the cost of political reorganization.

### [uxxbslyr] Vibrate only on autocorrect

A soft keyboard for touchscreen input should have a setting that causes it to vibrate only when autocorrect occurs.  Motivation is to avoid things autocorrecting badly.

## Friday, July 27, 2018

### [yxswgwqe] Use Unicode as little as possible

Unicode, by its charter, provides "as much as possible", the union of all existing character sets and symbols.  That doesn't mean you should use it as much as possible.  In fact, you should be conservative in how much of it you use, using the minimum necessary to accomplish your communication goal.  The recipient might not have as much Unicode support as you were hoping, and a channel using lots of Unicode is vulnerable to attacks like homograph attacks.

This is kind of a variation on, be liberal in what you accept, be conservative in what you do.

## Wednesday, July 25, 2018

### [bmjqznnm] 1812 Karaoke

Create a recording of the 1812 Overture missing the cannon shots, which can be remixed by others adding interesting sound effects where the cannons would go.  Perhaps someone has a cannon but no orchestra.

## Wednesday, July 18, 2018

### [yipmwzjx] ATM coins

Combine the functions of a change machine and ATM to withdraw exact change.

Dollar bills are difficult for machines to handle, but dollar coins should be easy.

### [ktjcofvo] Planets in a dense starfield

If a planet is in front of a dense starfield, can one (with an amateur telescope) watch the planet wander in front of the stars in real time?

The center of the Milky Way is dense.  The ecliptic intersects it in Sagittarius and Scorpius.  The disc of the galaxy in the outward direction are the constellations Gemini and Taurus.  Anything else: star clusters?

The glare of the sun probably washes out stars behind Mercury.

### [sreubrxp] Multiple highest factor

Numbers which are not a perfect power of a prime, and whose largest prime factor has exponent greater than 1.  One can normally omit the largest factor when giving a prime factorization of a number, but here it is not clear what that means.

f(x)=local(m,s);m=factorint(x);s=matsize(m);if(s[1]==1,0,if(m[s[1],2]==1,0,1))

18 36 50 54 72 75 98 100 108 144 147 150 162 196 200 216 225 242 245 250 288 294 300 324 338 363 375 392 400 432 441 450 484 486 490 500 507 576 578 588 600 605 648 675 676 686 722 726 735 750 784 800 845 847 864 867 882 900 968 972 980 1000 1014 1029 1058 1083 1089 1125 1152 1156 1176 1183 1200 1210 1225 1250 1296 1323 1350 1352 1372 1444 1445 1452 1458 1470 1500 1521 1568 1587 1600 1682 1690 1694 1715 1728 1734 1764 1800 1805 1815 1859 1875 1922 1936 1944 1960 2000 2023 2025 2028 2058 2116 2166 2178 2205 2250 2304 2312 2352 2366 2400 2420 2450 2500 2523 2527 2535 2541 2592 2601 2645 2646 2662 2700 2704 2738 2744 2883 2888 2890 2904 2916 2940 3000 3025 3042 3087 3136 3174 3179 3200 3249 3267 3362 3364 3375 3380 3388 3430 3456 3468 3528 3549 3600 3610 3630 3675 3698 3703 3718 3750 3757 3844 3872 3888 3920 3969 3971 3993 4000 4046 4050 4056 4107 4116 4205 4225 4232 4235 4332 4335 4356 4374 4394 4410 4418 4500 4563 4608 4624 4693 4704 4732 4761 4800 4802 4805 4840 4900 5000 5043 5046 5054 5070 5082 5145 5184 5202 5290 5292 5324 5400 5408 5415 5445 5476 5488 5547 5577 5618 5625 5766 5776 5780 5808 5819 5832 5880 5887 5915 5929 6000 6050 6069 6075 6084 6125 6137 6174 6250 6272 6348 6358 6400 6498 6534 6591 6615 6627 6655 6724 6727 6728 6750 6760 6776 6845 6860 6877 6912 6936 6962 7056 7098 7200 7203 7220 7225 7260 7350 7396 7406 7436 7442 7500 7514 7569 7581 7605 7623 7688 7744 7776 7803 7840 7935 7938 7942 7986 8000 8092 8100 8112 8214 8232 8281 8405 8410 8427 8450 8464 8470 8575 8649 8664 8670 8712 8748 8788 8820 8836 8978 8993 9000 9025 9075 9126 9216 9245 9248 9251 9261 9295 9317 9375 9386 9408 9464 9522 9537 9583 9600 9604 9610 9680 9747 9800 9801 9826 10000

## Tuesday, July 17, 2018

### [qxswupcu] staple and unstaple are gone

The source code to staple and unstaple, programs for the all or nothing transform, seems gone from the internet.

Too bad if you have a stapled file that is now unreadable.

Is there no longer any interest in AoNT?  Seems like a useful primitive that one would expect many (incompatible, pessimistically) implementations.  Rivest's original paper has a pretty clear description.  Did staple use Rivest's algorithm?

### [zbnwixis] 2D Recaman sequence

Modify the Recaman sequence OEIS A005132 to travel between points on a 2D lattice instead of integers on the number line. The jump sizes increase according to the square roots of OEIS A001481, numbers which are the sum of 2 squares.  There are many jumps (usually at least 8) possible: choose the jump to the point that hasn't been previously visited that gets closest to the origin.

What should be done if there are many valid points that are equal distance to the origin?  Some possibilities:

1. Jump to all of them: it's no longer a sequence but a tree.  Actually digraph because two braches could simultaneously jump to the same point.
2. Choose the one that's closest to the previous point.  Break ties by going further back in time.
3. Or farthest.
4. Closest to any previous point.  Break ties by considering the second closest previously visited point, etc.
5. Or farthest.

Incidentally, we could terminate the 1D Recaman sequence when the jump forward or backward are both numbers which have already been visited.  The sequence would terminate before the second 42.  If we want a longer sequence, the jump sizes probably have to grow faster than 1,2,3,...  Maybe skip that jump size?  Then what is the rate of growth of the jump sizes?

Consider using the same termination criterion, terminate if no jumps possible, for branches of the tree in possibilty 1 above.

### [cjlmoizr] The thrill is gone

Did you actually enjoy something, or did you just fool yourself into thinking you enjoyed it?  Maybe the latter because you've enjoyed it in the past, or you feel you are supposed to (by social pressure) enjoy it.

Perhaps an easy way to tell: are you still happy the next day?

What causes the sensation of "still happy the next day"?  What causes it not to happen?  Is it a good way to measure whether you actually enjoyed something?  Can you tell in the moment whether you will be happy the next day?

## Monday, July 16, 2018

### [mcwnlliy] On the width of a Gaussian Moat

TSUCHIMURA, Nobuyuki, "Computational Results for the Gaussian Moat Problem," https://www.keisu.t.u-tokyo.ac.jp/data/2004/METR04-13.pdf

Tsuchimura uses the term "width" in an unusual way, different from the popular meaning of "width".  To distinguish the two meanings where there might be ambiguity, we will write "technical width" for the sense used by Tsuchimura and we will write "popular width" to mean the meaning of "width" as popularly understood: the Euclidean distance (by the Pythagorean theorem) between two Gaussian primes on either side of the moat at its narrowest point (strait).

"Technical width" is synonymous with the step size k, in particular, the step size which failed to walk to infinity.  Therefore, when Tsuchimura establishes the existence of a moat of technical width sqrt(36)=6, it means that the algorithm walking outwards with a step size of 6 terminated; that is, it discovered a moat of popular width strictly greater than than 6, because step size 6 was not enough to cross it.  A step size of 6 gets you around the connected component inside the moat, but not across it.  The technical width of the moat is 6; the popular width is 6+delta.

Because of the discreteness of the Gaussian Moat Problem, we know (or have a very good guess) what that value of 6+delta is.  The next largest number after 6=sqrt(36) is sqrt(37).  However, because Gaussian primes (other than 1+i and its symmetries) all have the same checkerboard parity, the next largest possible distance between Gaussian primes is sqrt(40).  It could be that the popular width of the moat is even larger than sqrt(40), but that would be highly unlikely: whenever the step size is increased, the frontier increases dramatically.

The sequence of possible moat widths (squared) is OEIS A128106.  The popular width is one sequence element after the technical width.

To summarize, the result of Tsuchimura is that a moat of technical width 6, or a moat of popular width sqrt(40) separates the origin from infinity.  The current unsolved problem is whether a step size of sqrt(40) is sufficient to get to infinity (but the smart money is on "no", i.e., there exists a moat of technical width sqrt(40).).

The current Gaussian moat Wikipedia article includes an illustration of a moat with the caption explaining the moat has width 2.  This 2 is the popular width.  The same moat, with "Total size of the component" of 14, is listed as k=sqrt(2) in Tsuchimura's paper.

The previous paper,

Gethner, Wagon, and Wick, "A Stroll through the Gaussian Primes"

does not use the word width to mean technical width.  Instead, it refers to a moat with technical width X as an X-moat.  Incidentally, the paper illustrates that the connected component for various given step sizes have interesting shapes.

Incidentally, one cannot reach anywhere from the origin stepping only on Gaussian primes, because the origin, 0+0i, is itself not prime.

### [xjzqtjzg] Top-heavy perfect powers

Below are a list of perfect powers b^n (b<=n) in increasing order, up to a googol.  There are 2413 values.  The list omits bases which are perfect powers themselves, e.g., 4^n, 8^n, 9^n.

Here is Haskell source code to compute the list.  We used functions from the data-ordlist package to merge an infinite list of ordered infinite lists into a single ordered list.  This seems to be a nontrivial function to write, having written it a few times ((1) and (2)) before discovering Data.List.Ordered.  (Incidentally, data-ordlist is not indexed by Hoogle version 4.  It is indexed by the alpha version (Hoogle 5), but Hoogle 5 cannot search by type Ord a => [[a]] -> [a].)  We also used Data.List.Ordered.minus to compute the set difference of two infinite lists.

The motivation was to investigate increasing the breadth of the Cunningham project, which currently factors integers b^n +/- 1 with b restricted to {2, 3, 5, 6, 7, 10, 11, 12}.  Within the original Cunningham range up to about 2^1200, there are 4357 perfect powers in the restricted set, but there would be 19256 in our expanded set.

What is the growth rate of this sequence?

2^2 2^3 2^4 3^3 2^5 2^6 3^4 2^7 3^5 2^8 2^9 3^6 2^10 2^11 3^7 5^5 2^12 3^8 2^13 5^6 2^14 3^9 2^15 6^6 3^10 2^16 5^7 2^17 3^11 2^18 6^7 5^8 2^19 3^12 7^7 2^20 3^13 6^8 5^9 2^21 2^22 3^14 7^8 2^23 5^10 6^9 3^15 2^24 2^25 7^9 3^16 5^11 6^10 2^26 3^17 2^27 5^12 2^28 7^10 6^11 3^18 2^29 2^30 3^19 5^13 7^11 2^31 6^12 3^20 2^32 5^14 2^33 10^10 3^21 6^13 7^12 2^34 5^15 3^22 2^35 2^36 6^14 3^23 7^13 10^11 2^37 5^16 2^38 3^24 11^11 6^15 2^39 7^14 5^17 3^25 10^12 2^40 2^41 3^26 6^16 11^12 5^18 2^42 7^15 3^27 2^43 12^12 10^13 6^17 2^44 5^19 3^28 7^16 11^13 2^45 3^29 2^46 5^20 10^14 6^18 12^13 2^47 3^30 7^17 2^48 13^13 11^14 5^21 2^49 6^19 3^31 10^15 2^50 12^14 7^18 3^32 2^51 5^22 6^20 13^14 11^15 2^52 3^33 2^53 10^16 14^14 7^19 5^23 12^15 3^34 2^54 6^21 2^55 11^16 3^35 13^15 5^24 2^56 7^20 10^17 6^22 2^57 3^36 14^15 12^16 2^58 5^25 15^15 3^37 11^17 7^21 2^59 13^16 6^23 10^18 2^60 3^38 5^26 14^16 12^17 2^61 7^22 3^39 2^62 6^24 11^18 15^16 5^27 13^17 2^63 10^19 3^40 2^64 12^18 7^23 6^25 14^17 3^41 2^65 5^28 11^19 2^66 15^17 10^20 3^42 13^18 2^67 6^26 5^29 7^24 2^68 12^19 3^43 14^18 2^69 11^20 17^17 5^30 3^44 10^21 6^27 2^70 7^25 13^19 15^18 2^71 3^45 12^20 5^31 2^72 14^19 6^28 11^21 3^46 7^26 2^73 10^22 17^18 2^74 13^20 15^19 5^32 3^47 6^29 2^75 18^18 12^21 7^27 2^76 3^48 11^22 14^20 10^23 5^33 2^77 6^30 17^19 3^49 13^21 2^78 15^20 7^28 12^22 5^34 2^79 18^19 3^50 11^23 10^24 14^21 2^80 6^31 19^19 3^51 2^81 5^35 13^22 7^29 17^20 2^82 15^21 3^52 12^23 6^32 2^83 11^24 10^25 18^20 5^36 14^22 2^84 3^53 7^30 19^20 2^85 13^23 6^33 3^54 17^21 5^37 15^22 2^86 12^24 10^26 20^20 11^25 2^87 7^31 3^55 18^21 14^23 6^34 2^88 5^38 3^56 13^24 2^89 19^21 12^25 10^27 7^32 15^23 17^22 11^26 2^90 3^57 6^35 5^39 20^21 2^91 14^24 18^22 3^58 2^92 21^21 13^25 7^33 5^40 2^93 10^28 6^36 12^26 11^27 19^22 3^59 15^24 2^94 17^23 2^95 20^22 3^60 14^25 5^41 7^34 6^37 18^23 2^96 13^26 10^29 21^22 3^61 12^27 11^28 2^97 5^42 15^25 19^23 2^98 17^24 22^22 6^38 7^35 3^62 14^26 2^99 20^23 10^30 5^43 3^63 13^27 2^100 18^24 11^29 12^28 6^39 2^101 21^23 7^36 3^64 15^26 19^24 2^102 5^44 17^25 22^23 14^27 10^31 2^103 3^65 6^40 13^28 20^24 11^30 7^37 12^29 2^104 23^23 18^25 5^45 3^66 2^105 21^24 15^27 6^41 2^106 3^67 19^25 17^26 10^32 14^28 7^38 5^46 2^107 22^24 11^31 13^29 12^30 3^68 2^108 20^25 18^26 23^24 6^42 2^109 5^47 3^69 15^28 7^39 10^33 21^25 2^110 24^24 17^27 14^29 19^26 11^32 3^70 2^111 13^30 12^31 6^43 5^48 22^25 2^112 7^40 20^26 3^71 18^27 10^34 2^113 23^25 15^29 6^44 5^49 2^114 3^72 11^33 21^26 14^30 17^28 24^25 19^27 13^31 12^32 2^115 7^41 3^73 22^26 2^116 5^50 10^35 6^45 20^27 18^28 2^117 15^30 3^74 23^26 11^34 7^42 2^118 14^31 12^33 13^32 5^51 17^29 21^27 3^75 6^46 19^28 2^119 24^26 10^36 2^120 22^27 3^76 7^43 5^52 18^29 2^121 20^28 11^35 15^31 6^47 14^32 12^34 2^122 3^77 13^33 23^27 26^26 17^30 10^37 21^28 2^123 5^53 19^29 7^44 3^78 24^27 2^124 6^48 11^36 22^28 2^125 15^32 18^30 3^79 20^29 5^54 12^35 14^33 13^34 2^126 10^38 7^45 23^28 6^49 17^31 3^80 26^27 2^127 21^29 19^30 5^55 11^37 2^128 24^28 3^81 15^33 2^129 12^36 7^46 6^50 18^31 22^29 14^34 13^35 10^39 20^30 3^82 2^130 5^56 17^32 2^131 23^29 11^38 3^83 26^28 19^31 21^30 6^51 7^47 2^132 5^57 12^37 15^34 10^40 24^29 2^133 3^84 13^36 14^35 18^32 22^30 20^31 2^134 6^52 28^28 5^58 3^85 7^48 17^33 11^39 2^135 23^30 19^32 2^136 21^31 10^41 12^38 3^86 26^29 15^35 13^37 5^59 2^137 6^53 14^36 24^30 7^49 18^33 3^87 2^138 22^31 20^32 11^40 17^34 2^139 5^60 28^29 3^88 10^42 6^54 12^39 2^140 19^33 23^31 7^50 21^32 13^38 15^36 14^37 29^29 2^141 26^30 3^89 5^61 18^34 11^41 2^142 24^31 6^55 20^33 3^90 22^32 10^43 2^143 17^35 7^51 12^40 5^62 2^144 28^30 3^91 13^39 19^34 15^37 14^38 23^32 6^56 21^33 2^145 11^42 26^31 29^30 3^92 18^35 7^52 2^146 10^44 5^63 24^32 20^34 12^41 2^147 17^36 22^33 30^30 6^57 3^93 2^148 13^40 15^38 14^39 5^64 19^35 11^43 7^53 3^94 2^149 28^31 23^33 21^34 10^45 6^58 2^150 18^36 26^32 12^42 3^95 29^31 5^65 2^151 17^37 20^35 24^33 7^54 22^34 13^41 2^152 30^31 3^96 11^44 14^40 15^39 6^59 10^46 19^36 2^153 5^66 31^31 21^35 3^97 23^34 28^32 2^154 12^43 18^37 7^55 2^155 6^60 26^33 17^38 3^98 13^42 29^32 5^67 20^36 11^45 24^34 2^156 22^35 14^41 10^47 15^40 3^99 2^157 30^32 19^37 7^56 6^61 12^44 5^68 2^158 21^36 23^35 18^38 3^100 31^32 28^33 2^159 13^43 11^46 17^39 10^48 26^34 14^42 20^37 2^160 7^57 3^101 15^41 5^69 6^62 29^33 24^35 22^36 2^161 12^45 19^38 3^102 30^33 2^162 21^37 5^70 11^47 18^39 10^49 13^44 7^58 23^36 6^63 2^163 3^103 28^34 31^33 17^40 14^43 2^164 15^42 20^38 26^35 3^104 5^71 12^46 22^37 2^165 24^36 29^34 6^64 7^59 19^39 2^166 11^48 10^50 3^105 33^33 13^45 18^40 30^34 21^38 2^167 5^72 23^37 14^44 17^41 15^43 2^168 3^106 6^65 28^35 7^60 31^34 12^47 20^39 2^169 26^36 10^51 22^38 5^73 11^49 3^107 24^37 19^40 2^170 29^35 13^46 6^66 18^41 2^171 3^108 7^61 21^39 14^45 33^34 17^42 30^35 5^74 23^38 15^44 2^172 12^48 10^52 3^109 20^40 11^50 34^34 2^173 28^36 6^67 31^35 26^37 22^39 13^47 2^174 7^62 5^75 19^41 24^38 3^110 29^36 2^175 18^42 14^46 12^49 21^40 17^43 6^68 15^45 3^111 2^176 10^53 23^39 11^51 5^76 33^35 30^36 7^63 2^177 20^41 3^112 13^48 28^37 2^178 34^35 31^36 6^69 22^40 19^42 26^38 5^77 24^39 14^47 2^179 3^113 12^50 18^43 10^54 35^35 7^64 15^46 29^37 17^44 11^52 2^180 21^41 3^114 23^40 6^70 2^181 5^78 13^49 20^42 30^37 33^36 2^182 3^115 7^65 19^43 28^38 10^55 14^48 12^51 22^41 2^183 34^36 31^37 26^39 11^53 24^40 5^79 18^44 6^71 15^47 3^116 17^45 2^184 21^42 29^38 35^36 2^185 13^50 7^66 3^117 23^41 5^80 20^43 2^186 10^56 6^72 12^52 30^38 14^49 33^37 11^54 19^44 2^187 3^118 22^42 28^39 15^48 18^45 24^41 2^188 26^40 17^46 5^81 7^67 34^37 31^38 3^119 6^73 13^51 21^43 2^189 10^57 29^39 35^37 23^42 2^190 12^53 20^44 3^120 11^55 14^50 5^82 7^68 2^191 19^45 6^74 30^39 15^49 33^38 22^43 3^121 18^46 2^192 17^47 28^40 13^52 24^42 10^58 26^41 5^83 37^37 2^193 31^39 21^44 34^38 3^122 12^54 7^69 11^56 6^75 2^194 14^51 29^40 20^45 23^43 35^38 3^123 2^195 5^84 15^50 19^46 18^47 10^59 2^196 13^53 17^48 22^44 30^40 6^76 7^70 3^124 33^39 2^197 28^41 24^43 12^55 11^57 5^85 26^42 21^45 37^38 14^52 2^198 3^125 31^40 34^39 20^46 2^199 23^44 6^77 29^41 15^51 10^60 7^71 38^38 19^47 5^86 3^126 13^54 2^200 35^39 18^48 17^49 11^58 22^45 12^56 2^201 30^41 3^127 6^78 24^44 33^40 14^53 28^42 2^202 5^87 21^46 26^43 7^72 10^61 3^128 2^203 31^41 20^47 15^52 37^39 34^40 13^55 23^45 19^48 2^204 29^42 11^59 6^79 18^49 5^88 12^57 17^50 3^129 38^39 7^73 2^205 22^46 35^40 14^54 10^62 2^206 3^130 30^42 39^39 24^45 21^47 5^89 28^43 6^80 26^44 33^41 2^207 15^53 13^56 20^48 11^60 3^131 7^74 12^58 2^208 31^42 23^46 19^49 37^40 17^51 18^50 34^41 29^43 5^90 2^209 3^132 10^63 6^81 14^55 22^47 38^40 2^210 35^41 7^75 3^133 21^48 24^46 13^57 15^54 30^43 2^211 11^61 5^91 39^40 12^59 26^45 28^44 20^49 33^42 6^82 2^212 3^134 19^50 17^52 10^64 23^47 18^51 40^40 2^213 31^43 14^56 7^76 37^41 5^92 34^42 29^44 3^135 2^214 22^48 11^62 6^83 13^58 15^55 2^215 12^60 38^41 21^49 35^42 24^47 3^136 30^44 10^65 5^93 2^216 20^50 7^77 26^46 28^45 17^53 19^51 39^41 18^52 33^43 2^217 14^57 23^48 6^84 3^137 11^63 31^44 2^218 40^41 5^94 13^59 22^49 29^45 12^61 3^138 34^43 15^56 37^42 7^78 2^219 10^66 21^50 41^41 6^85 2^220 24^48 3^139 38^42 20^51 35^43 5^95 17^54 30^45 14^58 19^52 26^47 2^221 18^53 28^46 11^64 23^49 7^79 3^140 33^44 39^42 2^222 13^60 12^62 6^86 10^67 15^57 5^96 31^45 22^50 2^223 29^46 3^141 40^42 34^44 2^224 37^43 21^51 7^80 14^59 24^49 20^52 17^55 11^65 6^87 2^225 41^42 3^142 19^53 18^54 5^97 26^48 38^43 35^44 30^46 13^61 12^63 10^68 28^47 2^226 23^50 42^42 15^58 3^143 33^45 2^227 39^43 7^81 22^51 6^88 5^98 31^46 2^228 3^144 11^66 29^47 21^52 14^60 40^43 17^56 34^45 2^229 20^53 10^69 37^44 24^50 18^55 19^54 13^62 12^64 3^145 5^99 2^230 6^89 7^82 26^49 41^43 15^59 30^47 23^51 28^48 35^45 38^44 2^231 3^146 11^67 42^43 22^52 2^232 33^46 5^100 14^61 10^70 39^44 6^90 21^53 31^47 17^57 3^147 2^233 7^83 12^65 13^63 29^48 43^43 20^54 18^56 19^55 24^51 2^234 34^46 40^44 15^60 37^45 5^101 3^148 2^235 26^50 23^52 6^91 11^68 30^48 28^49 41^44 7^84 10^71 35^46 2^236 14^62 38^45 3^149 22^53 12^66 13^64 5^102 2^237 17^58 33^47 21^54 42^44 18^57 20^55 3^150 31^48 6^92 39^45 19^56 2^238 29^49 15^61 24^52 7^85 11^69 43^44 2^239 34^47 5^103 10^72 3^151 40^45 37^46 26^51 23^53 14^63 2^240 12^67 44^44 28^50 6^93 30^49 13^65 22^54 3^152 2^241 35^47 41^45 17^59 38^46 7^86 5^104 21^55 18^58 2^242 20^56 33^48 19^57 11^70 15^62 3^153 10^73 42^45 31^49 29^50 6^94 2^243 24^53 39^46 14^64 12^68 5^105 2^244 3^154 43^45 34^48 13^66 7^87 23^54 26^52 40^46 37^47 2^245 28^51 17^60 22^55 30^50 6^95 11^71 3^155 44^45 10^74 21^56 2^246 18^59 5^106 15^63 35^48 20^57 19^58 41^46 38^47 2^247 7^88 45^45 33^49 3^156 12^69 14^65 24^54 31^50 29^51 13^67 2^248 42^46 6^96 39^47 5^107 23^55 3^157 2^249 11^72 26^53 10^75 34^49 17^61 43^46 22^56 7^89 28^52 2^250 15^64 37^48 40^47 18^60 30^51 21^57 3^158 19^59 20^58 6^97 5^108 12^70 2^251 44^46 14^66 35^49 13^68 41^47 38^48 2^252 3^159 24^55 33^50 10^76 11^73 29^52 45^46 7^90 31^51 2^253 5^109 23^56 6^98 17^62 42^47 3^160 39^48 26^54 15^65 2^254 46^46 22^57 18^61 34^50 12^71 21^58 28^53 19^60 20^59 2^255 43^47 14^67 30^52 3^161 37^49 13^69 5^110 40^48 7^91 10^77 6^99 11^74 2^256 35^50 44^47 24^56 3^162 2^257 38^49 41^48 33^51 29^53 17^63 31^52 5^111 23^57 15^66 2^258 45^47 12^72 7^92 3^163 6^100 26^55 18^62 22^58 42^48 14^68 39^49 2^259 13^70 10^78 19^61 21^59 20^60 11^75 34^51 28^54 46^47 3^164 2^260 5^112 30^53 43^48 37^50 40^49 2^261 47^47 6^101 7^93 24^57 3^165 35^51 17^64 12^73 15^67 2^262 44^48 33^52 29^54 23^58 5^113 38^50 10^79 41^49 31^53 18^63 14^69 13^71 11^76 2^263 3^166 22^59 26^56 19^62 21^60 45^48 20^61 6^102 7^94 2^264 42^49 39^50 28^55 34^52 3^167 5^114 30^54 2^265 46^48 12^74 15^68 37^51 17^65 10^80 43^49 24^58 2^266 40^50 6^103 3^168 11^77 13^72 14^70 47^48 7^95 35^52 18^64 23^59 2^267 5^115 29^55 33^53 44^49 31^54 22^60 19^63 38^51 3^169 41^50 26^57 21^61 20^62 2^268 48^48 6^104 12^75 2^269 10^81 45^49 28^56 5^116 3^170 7^96 39^51 15^69 42^50 34^53 17^66 11^78 30^55 2^270 13^73 14^71 24^59 46^49 37^52 2^271 3^171 18^65 43^50 23^60 40^51 6^105 5^117 35^53 19^64 2^272 22^61 29^56 47^49 20^63 7^97 21^62 33^54 10^82 12^76 31^55 3^172 26^58 38^52 44^50 2^273 41^51 11^79 15^70 48^49 13^74 17^67 5^118 2^274 6^106 28^57 14^72 3^173 45^50 34^54 30^56 39^52 2^275 42^51 24^60 7^98 18^66 10^83 3^174 23^61 2^276 12^77 37^53 19^65 46^50 5^119 22^62 6^107 20^64 21^63 43^51 40^52 11^80 29^57 35^54 2^277 26^59 3^175 15^71 31^56 33^55 13^75 47^50 7^99 14^73 17^68 2^278 38^53 44^51 41^52 5^120 28^58 3^176 2^279 10^84 6^108 48^50 18^67 12^78 24^61 30^57 34^55 2^280 45^51 39^53 11^81 19^66 42^52 23^62 3^177 7^100 20^65 22^63 5^121 2^281 21^64 13^76 15^72 37^54 46^51 14^74 6^109 29^58 2^282 26^60 17^69 40^53 35^55 3^178 43^52 50^50 10^85 31^57 33^56 2^283 12^79 5^122 47^51 38^54 7^101 18^68 28^59 11^82 3^179 44^52 41^53 2^284 24^62 6^110 30^58 19^67 48^51 34^56 13^77 23^63 2^285 15^73 20^66 3^180 22^64 39^54 21^65 14^75 45^52 5^123 10^86 42^53 2^286 17^70 7^102 37^55 29^59 26^61 12^80 3^181 6^111 2^287 11^83 46^52 35^56 31^58 40^54 33^57 43^53 18^69 50^51 5^124 2^288 28^60 3^182 13^78 38^55 47^52 24^63 19^68 2^289 10^87 15^74 7^103 51^51 41^54 44^53 14^76 30^59 23^64 6^112 20^67 22^65 21^66 34^57 2^290 3^183 17^71 5^125 12^81 48^52 11^84 39^55 2^291 45^53 42^54 26^62 29^60 3^184 37^56 18^70 7^104 2^292 6^113 31^59 10^88 13^79 35^57 5^126 33^58 40^55 46^53 2^293 15^75 43^54 19^69 14^77 3^185 28^61 24^64 50^52 38^56 20^68 12^82 2^294 23^65 11^85 21^67 17^72 22^66 47^53 30^60 41^55 6^114 7^105 3^186 44^54 5^127 51^52 2^295 34^58 10^89 39^56 2^296 48^53 13^80 18^71 26^63 29^61 3^187 52^52 45^54 42^55 15^76 37^57 14^78 2^297 5^128 31^60 6^115 19^70 35^58 11^86 12^83 7^106 33^59 3^188 2^298 24^65 40^56 28^62 20^69 46^54 17^73 43^55 23^66 21^68 22^67 10^90 2^299 50^53 38^57 30^61 5^129 3^189 13^81 6^116 47^54 2^300 41^56 34^59 18^72 44^55 7^107 51^53 14^79 26^64 15^77 11^87 2^301 12^84 3^190 29^62 39^57 48^54 19^71 5^130 42^56 2^302 45^55 52^53 37^58 31^61 10^91 6^117 17^74 20^70 24^66 35^59 33^60 3^191 28^63 2^303 21^69 23^67 7^108 22^68 40^57 13^82 53^53 46^55 43^56 2^304 5^131 30^62 3^192 38^58 18^73 11^88 14^80 12^85 15^78 50^54 2^305 6^118 34^60 41^57 47^55 26^65 10^92 44^56 19^72 3^193 2^306 7^109 29^63 51^54 5^132 39^58 17^75 20^71 2^307 13^83 31^62 48^55 24^67 37^59 42^57 21^70 3^194 45^56 23^68 6^119 28^64 22^69 33^61 35^60 52^54 11^89 2^308 12^86 14^81 18^74 15^79 40^58 7^110 5^133 10^93 2^309 3^195 30^63 43^57 53^54 46^56 38^59 2^310 19^73 6^120 26^66 34^61 50^55 17^76 3^196 41^58 54^54 13^84 29^64 2^311 47^56 5^134 20^72 44^57 11^90 7^111 24^68 39^59 21^71 12^87 51^55 2^312 31^63 23^69 22^70 14^82 3^197 10^94 28^65 15^80 37^60 18^75 33^62 42^58 48^56 6^121 35^61 2^313 45^57 5^135 52^55 3^198 40^59 2^314 30^64 19^74 7^112 13^85 43^58 17^77 11^91 46^57 38^60 26^67 2^315 53^55 6^122 3^199 34^62 12^88 20^73 10^95 29^65 5^136 2^316 14^83 50^56 41^59 21^72 24^69 15^81 54^55 47^57 22^71 44^58 23^70 18^76 3^200 2^317 31^64 39^60 7^113 28^66 51^56 37^61 33^63 6^123 55^55 2^318 35^62 5^137 42^59 13^86 11^92 48^57 45^58 3^201 19^75 17^78 10^96 30^65 2^319 12^89 52^56 40^60 26^68 14^84 20^74 2^320 7^114 38^61 43^59 3^202 15^82 46^58 5^138 34^63 6^124 29^66 21^73 53^56 24^70 2^321 22^72 18^77 23^71 41^60 50^57 11^93 3^203 13^87 2^322 31^65 28^67 44^59 47^58 10^97 54^56 39^61 12^90 5^139 33^64 19^76 7^115 17^79 37^62 2^323 6^125 35^63 51^57 3^204 42^60 14^85 55^56 30^66 48^58 2^324 45^59 20^75 15^83 26^69 40^61 3^205 52^57 2^325 21^74 5^140 11^94 56^56 18^78 38^62 29^67 24^71 22^73 10^98 43^60 34^64 13^88 7^116 23^72 6^126 46^59 2^326 12^91 53^57 3^206 41^61 28^68 31^66 17^80 2^327 19^77 50^58 5^141 14^86 44^60 39^62 47^59 33^65 2^328 54^57 3^207 15^84 37^63 35^64 6^127 7^117 20^76 11^95 30^67 10^99 42^61 2^329 51^58 26^70 13^89 21^75 18^79 45^60 48^59 55^57 3^208 5^142 12^92 40^62 22^74 2^330 24^72 23^73 29^68 38^63 52^58 34^65 6^128 2^331 43^61 56^57 17^81 14^87 3^209 7^118 19^78 46^60 28^69 31^67 2^332 5^143 15^85 11^96 41^62 10^100

## Sunday, July 15, 2018

### [cftaqxzh] Digit groupings of increasing size

Although grouping digits in groups of 3 is useful for quickly telling how large a medium-sized number is (perhaps up to a trillion = 1e12), after a number gets too large, it becomes difficult to count how many groups of three it has.  Therefore, consider grouping in larger chunks as the number gets larger.  Below we demonstrate grouping digits in groups of 3, 4, 8, 16, 32,... doubling in powers of 2.  The partial sums are powers of 2 minus 1, so it is easy to go from the number of groups to the total digits in them.

Could also do Fibonacci sequence, triangular numbers, square numbers.

Not sure how useful this is: for transcribing a number, digit groupings of constant size is best.  If you want to convey the order of magnitude of a number, scientific notation is best (or tetration).

Previously similar.

9,123 ~= 9e3

9,1234,123 ~= 9e7

9,12345678,1234,123 ~= 9e15

9,1234567890123456,12345678,1234,123 ~= 9e31

9,12345678901234567890123456789012,1234567890123456,12345678,1234,123 ~= 9e63

### [fxflbsnj] Constantly seated amusement park

The modern amusement park consists of a bunch of rides all of which are simply sit down and be shaken in various ways.  Take this concept to the extreme by getting strapped into a chair on rails at the entrance of the park, which drives around autonomously from ride to ride, with you never having to leave the chair: it hooks itself on to each ride.

You are perhaps presented with a menu of how you would like to be shaken next, and the chair takes you there.  It also intelligently schedules people to minimize waiting in line time.

Kind of like the chairs in WALL-E.

The opposite of sit and be shaken.

### [nyjlrefd] Right to life

Consider the three "inalienable rights" enumerated in the Declaration of Independence.  The right to the pursuit of happiness is hollow and meaningless; sure, you may pursue it in principle, but there is nothing stopping the government from putting obstacles in your pursuit.  We alienate people from their right to liberty all the time by prison.  Some jurisdictions, though not all, alienate people from their right to life by the death penalty.

Nevertheless, let us consider why and when a government should grant the right to life.

Knowing that the government cannot arbitrarily deprive you of your life induces or allows you to make better long-term plans.  Then, it is socially preferable to grant the right to life when knowing, or acknowledging, that you have that right affects your behavior.  By this logic, infanticide is acceptable: infants don't make plans.  (Abortion, any trimester, any means, is also acceptable.)  At what age are children capable of choosing delayed gratification?  Is this a good proxy for when you are able to make long-term plans for which a right to life is useful?  If so, this would be a threshold at which infanticide should forbidden.

Things might get more complicated when there are more stakeholders than just the person themselves living.  Perhaps these issues can be resolved through civil procedure.  However, inspired by the Coase Theorem, a government does have to set the default property line first.  It might still work out if the default property line is that no one has has the right to take the life of another, but those who sue for wrongful death have to show standing.

## Friday, July 13, 2018

### [qvhaepbp] Oven cooling fans and oven fires

Food in your oven has caught fire.  In the olden days, the right thing to do was to turn the oven off and wait: with the oven door shut, the fire will be deprived of oxygen and burn itself out.

Nowadays, modern ovens often have oven cooling fans to protect their electronics; these fans run even when the oven is switched off.  Such a fan continuously pumps oxygen into a fire in the oven and pumps smoke out of the oven into the living area.  Both of these seem very problematic: you've created a fireplace.

Ideally, the air pathway of the oven cooling fan cooling its electronics is isolated from the cooking chamber of the oven.  We have observed this to be false in practice: when the fan turned on, the flames of the food on fire grew and smoke poured out of the cooling fan vent.

Instructions on dealing with oven fires give contradictory instructions: do not open the oven door because of danger that the fire will flash and burn you due to the sudden influx of air, and use a fire extinguisher.  However, a fire extinguisher cannot be used on burning food inside the oven without opening the door.  I suspect the contradiction is supposed to be resolved as follows: if the fire minor, it will burn itself out with the oven switched off and the door kept closed.  If the fire is major, it is worth the risk of harm to oneself in opening the door and using a fire extinguisher on it.  This is a bad situation because a typical person who only rarely deals with oven fires cannot accurately judge minor versus major and cannot accurately judge the risk/benefit tradeoff of opening the door.  With an oven-cooling fan possibly feeding a self-sustaining fire inside the oven, this decision becomes even more difficult.

One could pull the circuit breaker, shutting off the oven cooling fan.  Again, this is a difficult decision: is the decreased airflow to the oven fire and consequent possible more rapid extinguishing through oxygen deprivation worth the increased chance of damage to the oven electronics, the latter likely requiring very expensive oven repair or replacement?

## Wednesday, July 11, 2018

### [qnhyarna] Entertainment causality

Are you as an entertainer making people happy, or did you just happen to be in the right place at the right time with people who were destined to be happy?

### [khqsssse] Some easy chess problem types

1. Mate in 1
2. Series mate in 2
3. Helpmate in 1
4. Series mate in 3
5. Mate in 2

Mate in N of course helps orthodox chess skills.  Series mate in N also helps in learning to make plans.  Helpmate in 1 is good for learning to avoid blundering into a mate in 1 in orthodox chess.

What next?  Find the one move that blunders into a mate in 2: this type of problem does not have a name.  It is different from helpmate in 2 because that requires blundering twice.

### [ltxvlhld] The temperature of the Beast

(Body temperature) - (Freezing point of water) = 666 decidegrees Fahrenheit

### [idrdhpwa] Key stretching in Perl

Below is a demonstration of how to use Perl's crypt function to generate a SHA-256 password hash stretched to 654321 iterations.

(Previously similar, in Python.)  Perl may be better than Python for this because setting user passwords often happens very early during or after installation of a system, when Python (nor the mkpasswd utility in the whois package) might not yet be installed, but Debian even in its most minimal installation configuration always installs Perl.

Unlike Python, Perl does not have a built-in "make random salt" function, so we make it ourselves out of bytes read out of /dev/urandom.  Maybe we should have an option to manually specify the salt.

We permit retyping the password as many times as you want, in contrast to 2 times in typical password-setting procedures.  More than twice decreases the chance of typing it wrong accidentally twice, a fluke that is unsettlingly likely for a long password.  The password is echoed as you type; if this is a danger, then use a separate utility that doesn't echo and pipe it in (The Unix Way).  Possible dangers include shoulder-surfing and the visible password persisting in memory, then swap, of terminal buffers, e.g., gnome-terminal or screen.  Incidentally, which terminals wipe and overwrite memory when clearing the screen (^L) or closing a window?

Typing (much) more than twice also allows learning it.

Maybe we should have had a separate program (The Unix Way) for typing the password multiple times, verifying they are identical.

At the top in the comments are instructions on attempting to avoid the password hash from hitting disk.  (/run/shm can get swapped to disk, though, so it's not attempting too hard.)  These instructions are little bit silly because the hash eventually must hit disk in /etc/shadow.

```#! perl -wl
# mkdir /run/shm/me
# chmod go-rwx /run/shm/me
# sudo usermod -p \$(cat /run/shm/me/passwd) username
# rm -fr /run/shm/me
print STDERR "Keep repeatedly typing the password, or 'done':";
\$plain=<STDIN>;
chomp\$plain;
for(;;){
# Note: password will be echoed as you type.
\$verify=<STDIN>;
chomp\$verify;
last if \$verify eq "done";
die unless \$verify eq\$plain;
}
\$_=`dd if=/dev/urandom count=1`;
@random=unpack("C*",\$_);
die unless @random>=16;
#for(@random){    print "\$_\n"; }
@chars=("a".."z","A".."Z","0".."9",".","/");
die unless @chars==64;
for(0..15){
\$salt.=\$chars[\$random[\$_] & 63];
# we assume lower bits are just as random as upper, unlike LFSR PRNG.
}
#print\$salt;
\$type=5; #or 6
\$rounds=654321;
\$full='\$'.\$type."\\$rounds=\$rounds\\$".\$salt;
\$hash=crypt \$plain,\$full;
print\$hash;
```

## Tuesday, July 10, 2018

### [hivdeqyk] Adding apples and oranges

Declare Apple is_a Fruit. Declare Orange is_a Fruit.  1 * Apple + 2 * Orange = 3 * Fruit.  Without the is_a declarations, this would have failed with incompatible units.

Not sure what this would be useful for.

### [apmrwqek] Gender wage gap

The conventional hypothesis of why women earn less on average than men is that women leave the workplace for child care, therefore the employer does not long-term invest, e.g., on-the-job training, in female employees as much, leading to less promotion and raises.

Not all women leave the workplace for child care, so this is an imperfect information signaling game.  Are the signaling mechanisms working, or is there market failure?  What signaling mechanisms are happening?

Radical hypotheses: Lesbian, F2M transgender, might be groups less likely to have children.  It would be surprising if these are deliberate signaling, as they seem to be identity unrelated to employment signaling.

Also: A credible attitude of "I hate children" is pretty obvious as a signaling mechanism.

A hysterectomy or other irreversible procedure would be a very radical signaling mechanism, though unclear its cost outweighs the income benefits.  Are elective surgeries like this happening?  (Incidentally, if an employer wants to decrease the incidence of women leaving for child care so maximize their return on investment in the employee, they should definitely offer health insurance that covers abortions and birth control.  I'm surprised that prior to Obamacare, there weren't employers offering insurance that only covers abortions and birth control.)

Less radical (famous) hypothesis: education and training paid for by the employee.

We suspect the wage gap cannot be reduced to zero through signaling: signaling cannot be perfect, unless there is some risk other risk of leaving that men are more likely to have then women.  Maybe life expectancy?

A more sophisticated model does not assume that the decision to leave the workplace is deterministic: A women will compute expected future earnings and compare it with the utility of leaving the workplace for child care.  This can lead to a feedback effect: an employer promises low pay, the woman chooses to leave based on that (and prior to that, chooses not to invest in education), leading to the expectation among employers that women will leave, so employers give low pay.  Is this feedback effect causing market failure?

We suspect not: for any particular female employee, an employer can study the signals about the employee's relative utilities of money versus leaving for child care, and decide or decide not to pay an amount sufficient to keep the employee.  This is the same process as everyone else (i.e., men) in the labor market.  Once again, we need signaling to be accurate and precise.

## Monday, July 02, 2018

Big Dick Energy is synonymous with self-qi.

Thank you Anthony Bourdain for dying, inducing the term and concept to become well known?

### [xehndgkq] Git over sneakernet

Initial clone from Parent to Child: `git bundle create mybundle master` (as documented in git-bundle manpage).

"git pull" by Child from Parent: well documented in git-bundle manpage.

Move changes from Child to Parent: (on Child) `git format-patch origin/master -o patchdir`, transfer files in patchdir to Parent, (on Parent) `git am patchdir/*`

More conservatively, (on Parent) `git checkout -b temp-branch`, `git am` on temp-branch, merge temp-branch back on to master.

It can also be done both directions with git bundle: https://git-scm.com/book/en/v2/Git-Tools-Bundling

### [bscscrxl] Easy BOTW improvement ideas

Some ideas for "The Legend of Zelda: Breath of the Wild" that would have required very little additional programming by Nintendo to implement:

1. You can already replay most activities in the game as many times as you want: shrines, fighting enemies (because of the Blood Moon mechanic), including the final boss.  Extend repeatability to everything in the game: Ta'loh Naeg Teaching, Master Kohga, shrine and side quests (e.g., Naydra malice), Divine Beasts, Korok puzzles (but you don't reget the special rewards).  This allows the fun of easily trying different approaches to the same task, perhaps with abilities gained much later in the game.
2. Some way of changing the weather.  Exploration is the heart of the game, but some things can't be explored in certain weather.  This could be implemented as a more efficient "sleep until".  It's OK if this and other abilities below only become unlocked late in the game, perhaps after completing a lot.
3. Scroll through your Hyrule Compendium, and it highlights all the items within range of the Sheikah sensor.  This is so much more efficient than selecting and targeting each one.
4. More map stamps, beyond 100.
5. More camera photo storage space.
6. Get coordinates of your location, including elevation.  Maybe you have to learn to read Sheikah script.
7. Sheikah sensor detects goddess statues.
8. Sheikah sensor detects drops of enemies, for times when they roll away or get lost in tall grass.  (So all materials need compendium entries.)
9. You can buy the name, stats, and sensing ability of items in the Hyrule Compendium from Symin, but taking a picture remains your responsibility.  This leaves a challenge to 100%ing the game.
10. Further bomb power upgrades, to keep pace with the increasing HP of enemies.
11. Further upgrades on Stasis, increasing its time length.
12. Some way to increase your throwing strength / range.
13. More display cases at your house.  This allows challenging yourself by going on quests armed with very little, then coming back for all your stuff.
14. A bow that always slows down time.  You don't have to be in mid-air.
15. Some official way to fly.  The game engine can handle it, as demonstrated with stacked mine carts by Mety333.  One way is for Revali's Gale to be able to be reused while still in mid-air (combined with the fast recharge of Revali's Gale Plus).
16. Some way to decrease the automatic enemy strength (color) upgrades.  Although yes you've become stronger, it is annoying to have to fight the powerful ones all the time when you'd rather be exploring.  Easiest might be, enemy strength is scaled to the number of heart containers you have, which can be decreased at the Horned Statue.
17. Trigger a blood moon.  (Only after the "Under a Red Moon" shrine quest, to keep it from becoming too easy.)
18. Trigger a full recharge of a partially used champion's ability.
19. Read the durability remaining on a weapon.
20. More weapons stash space, using up all the Korok seeds.
21. All weapons respawn in the overworld (correcting oversights of Kite Shield, Forest Dweller's Sword, maybe some Lynel gear).
22. Award for discovering all treasures, for the 100% completionists.  I think the reason this doesn't exist is because there are a few glitched treasures which are impossible.
23. It takes less meat than fruit or vegetables to befriend a dog.
24. All dogs befriended award.
25. A dog at your house.
26. An alternative to the Champion's Tunic for getting enemy health, maybe an elixir.
27. Spacing the hearts in groups of 5, so you can easily count how many you have.  This mirrors the Stamina Wheel which is also in units of 5.
28. Have the Of The Wild set bonus Master Sword Beam Up increase its range to something ludicrous, like Bow of Light / Twilight Bow.  120 shrines was a lot of work.

## Saturday, June 23, 2018

### [hyklppdi] Sentence markup

Create a markup language in which sentences are semantically enclosed, so the user does not need to type capitalization of the first word of each sentence: this will be automatically done when the markup becomes rendered.

Motivation was that inserting a word at the beginning of a sentence annoyingly requires lowercasing the former first word.

Having sentences semantically enclosed with begin and end markers (tags) also allows modifying the amount of space between sentences (after periods) uniformly and with a single configuration change, and avoids difficulties regarding abbreviations with periods e.g. "e.g." in the middle of sentences.

Tricky situations: "Sentences in quotes."  (Sentences in parentheses.)  Extra space goes after, capitalization is not the first literal character.

We could also accomplish just the capitalization part (not sentence separating spaces) with a tag indicating "capitalize next word".

## Wednesday, June 20, 2018

### [lucddrvd] Hypercube nets

Build the collection of 261 octacubes that can be folded into a 4D tesseract.  (They are out of 3811 octacubes total.)  Maybe these give intuition about the fourth dimension.

Peter Turney, Unfolding the Tesseract, Journal of Recreational Mathematics, Vol. 17(1), 1984-85.  Has anyone else replicated/confirmed the count?

In 2D-3D, 11 out of 35 hexominoes are nets for the cube.

### [dvdotqbu] Life-sized procedurally generated world

Earth surface area is 5.1e14 m^2.  A high-resolution display has resolution 200 dpi, or 0.000127 meters per pixel.  We consider the task of generating a virtual world the size of earth at that resolution.

Earth surface area at that resolution would have 3.16e22 pixels.  This is equivalent in area to a circle with radius 1.00e11 (10^11) pixels.

Fractal terrain generation (e.g., plasma fractal) is ideal for this kind of task: terrain can be computed on demand at the resolution and location needed, never having to precompute nor store.  However, we will take a detour and consider the Mandelbrot set, a fractal different from the plasma fractal.  The Mandelbrot set has a fixed size, which is useful to get a sense of the scale needed to generate 10^22 pixels.  The Mandelbrot is contained within a circle of radius 2, so computing the Mandelbrot set with pixel spacing 2e-11 would yield 3.16e22 pixels.  (Incidentally, this spacing is well within double precision's 15 significant digits of precision, so no need for arbitrary precision arithmetic.)

### [tgsyrgxs] The Rubik's cube has too many colors

When in a scrambled state, the Rubik's cube is not pretty: it begs to be made prettier by solving it or turned into a pretty pattern, which can be psychologically frustrating (as OCD) if you can't solve it.

With fewer colors (some faces sharing colors), it might not look so chaotic in a scrambled state.  A cube with fewer colors can easily be constructed by restickering or disassembling multiple stickerless cubes.  This will also induce an easier puzzle.  The ultimate of course is the single color cube, which always looks the same and is trivial to solve.

We probably want just 2 or 3 colors.  Previously, exploring the different ways one can color the faces of a cube.

Maybe a different polyhedron than cube?

## Sunday, June 17, 2018

### [lkunovph] Throwing to maximize energy

How much kinetic energy can a human impart to a thrown ball, with no restrictions on the mass of the ball?  What mass maximizes?

Depends a bunch on throwing technique, especially running start.

### [ycgdwtri] Testing "Power corrupts"

Investigate as psychology research the adage "Power corrupts.  Absolute power corrupts absolutely."  How does it corrupt?  When does it corrupt?  At what rate does it corrupt?  What kinds of powers induce what kinds of corruption?  Does it depend on the "character" of the person before achieving power?

The Stanford Prison Experiment is the most famous experiment in this field.  Possibly flawed, but we need follow up investigation regardless to fine-tune our knowledge in this field: how should society design its structures of power?  (Optimistically, I hypothesize that society has organically discovered and implemented many mechanisms to counteract the effect despite not explicitly understanding it.)

Inspired as a response to Ben Blum "The lifespan of a lie", in which the author attempts to discredit the Stanford Prison Experiment and undermine its conclusions.  Curiously, the phrase "power corrupts" never appears in the piece, even though it is the central thesis of what the experiment was trying to prove.

It would be absolutely shocking if the adage were proven to be false in all respects, maybe always just an illusion of observer or selection bias, and that power actually does not affect psychology in any way.  Therefore, we assume the conclusions of the experiment remain valid -- power still corrupts.  Flaws in the experiment prevent strongly supporting the conclusion, but do not disprove it.

Blum's actual motive is far from disguised: it is highlighted in green in the middle of the piece.  The purpose of discrediting the experiment is to strengthen the political case for "individual responsibility", the propaganda technique employed by the right to justify maintaining racism and discrimination and cutting welfare.

By avoiding mentioning the issue "power corrupts", it also subtly supports another right-wing agenda item: the authoritarian state.  Perhaps we are meant to believe that power doesn't corrupt, so we should let our autocrats have as much power as they desire and nothing bad will happen.

### [gxuvwalk] A mobile population does not invest in local infrastructure

No incentive to politically support measures for long-term improvement of local infrastructure: they can just move elsewhere.  Tragedy of the commons but worse.

The easier it is to travel and move, the bigger government needs to be: the same government at both endpoints of the move.

### [oxgkyqgm] Mining human

Now that there are so many humans, one could imagine an entity (say, science-fiction aliens) mining humans on earth as a raw material.

We say "mining" not "farming" because, with so many available, the miners can act not worrying whether humans are a renewable resource.  (Maybe "hunting" is a better term, though that typically applies to creatures which require nontrivial effort to kill even one, but we imagine the aliens will mine humans en masse)  It'll be strip mining as humans live on the surface of the planet (for now), though for aliens from outer space, we live at the bottom of a deep gravity well, so maybe the mining metaphor is actually apt.

What are humans especially good for as a natural resource?  Not for meat: it'd be better (but by only by a factor of about 2) to abduct our cows or mine Antarctic krill, or take our arthropods or plants or bacteria.

Human brains are big and sophisticated: The Matrix (original draft) explored enslaving humans to use our brains as coprocessors.

Related to our brains being unique compared to other animals, the human skull is a uniquely shaped mass of bone, hollow, roughly spherical (therefore strong): maybe useful for something mechanical (a bearing?) or as a container.

Discard the rest of the body as mining tailings, kind of reminiscent of hunting elephants just for their tusks.  In fiction, this analogy could be made more obvious if the aliens mine us for an even smaller part of the human body, discarding the rest.

## Saturday, June 16, 2018

### [fxalwihm] Jury nullification, again

Back in the day, the fear (probably with actual instances) was that jury nullification would be used by jurors to refuse to convict a white (perhaps KKK) defendant on trial for lynching a black man.

Nowadays, the fear is that jurors will refuse to convict a cop on trial for shooting a black man.  History repeats itself.

It does illustrate how racial violence has been institutionalized: we have replaced lynch mobs with the police, both for the same purpose: instilling fear into African-Americans.

### [xdxghbpq] ilaoen shrudtu

Consider swapping the letter e, the most common letter of the alphabet, with the letter i, a narrow character in text especially sans serif, in order to pack information more densely.

Similarly, consider swapping the letter T (the second most common letter) with the letter L, which in lowercase is similarly narrow.  However, if the crossbar of the lowercase t is higher than the x height, and the t does not have a curved bottom, then kerning is often possible and the t will not consume much horizontal space.

Consedir swappeng lhi tillir i, lhi mosl common tillir of lhi atphabil, welh lhi tillir e, a narrow characlir en lixl ispiceatty sans siref, en ordir lo pack enformaleon mori dinsity.

Semetarty, consedir swappeng lhi tillir L (lhi sicond mosl common tillir) welh lhi tillir T, whech en towircasi es semetarty narrow.  Howivir, ef lhi crossbar of lhi towircasi l es heghir lhan lhi x hieghl, and lhi l dois nol havi a curvid bollom, lhin kirneng es oflin possebti and lhi l wett nol consumi much horezonlat spaci.

## Friday, June 15, 2018

### [bvopfken] Providing actual entertainment

To what extent is entertainment luring people with what they think they want, but actually providing something different, what they actually want but weren't aware they wanted it?

If true, why are people so out of touch with their true preferences?

Inspired by genre-crossing movies, e.g., the disaster/action story which is actually a love story.

## Thursday, June 14, 2018

### [lbyjcqtr] Literal Iron Chef

Competing metallurgists are provided with ore and asked to produce something, perhaps an alloy, which will be compared against the same the produced by competitors.

Competition over strength, yield, or other physical properties.

Generalizable to all chemistry.

Inspired by Gutenberg: could you make type metal from ore?

### [shkzjlob] Smallest factor music

Beats are numbered with consecutive integers.  On each beat, play a pitch corresponding to the least prime factor of the beat number.  Primes get a special sound.  Small factors occur often enough to sound like rhythmic accompaniment.

Could be done with a clock-like mechanical device.

### [muoxjpqg] More Rock Paper Scissors

Create a game like rochambo but for which a more complicated mixed strategy is optimal.  Avoid the incomplete information (the element of chance) of poker.

Easiest would be to adjust the payoff matrix.  Can it be done constraining the payoffs to be +1 or -1 only?

Not sure if this is possible.

### [sfnqcsnz] Fail and Royal Fail

Nickname the 7 high poker hand a "Fail", and 7 5 4 3 2, the worst possible hand, the "Royal Fail".

## Wednesday, June 13, 2018

### [jjklxjsr] When is group theory practically useful?

Primality proving: Examine the group structure of the multiplicative group (Z/nZ)* for the number n being tested (Lucas primality test, requiring factoring n-1).

To determine whether a polynomial of degree 5 or greater is solvable in radicals, examine the structure of its Galois group.  But there are many tricky details: General Formulas for Solving Solvable Sextic Equations, Thomas R. Hagedorn.

Examine the subgroups of a twisty puzzle like the Rubik's cube to find an admissable heuristic for A* search.

We do not include instances of group theory merely being used to prove a theorem, though the distinction is hazy ("prove that 17 is prime", "prove this algorithm is correct").

### [uytzvqqf] Wide and top-heavy Cunningham

We explore factoring numbers of the form b^n-1 and b^n+1, beyond the bases (namely beyond b= 2, 3, 5, 6, 7, 10, 11, or 12) investigated by the Cunningham Project.  We also impose the constraint of b<=n (top-heavy).

The general strategy was to use YAFU (but did not install ggnfs, so only SIQS).  YAFU was not exactly stable, occasionally segfaulting, aborting, or omitting small factors, so we took the medium-sized prime factors (primes which were 21 digits or more but not the final (largest) factor) found by YAFU and "polished" them to complete factorizations using Pari/GP: Load the medium-sized primes with addprimes, then factorint.  Polishing the list below took a little over an hour.  Passing the "1" flag to factorint (avoid MPQS) did not save any time even though we were looking only for small (20 digits or less) factors.

We omit printing the largest factor in the list below for brevity.  There is one prime (30^32+1) among the 2222 lines.  This is a fascinating number because it seems related to 2^32+1, the first composite Fermat number, with 3^32 and 5^32, the product of first 3 primes raised to the 32nd power.

This replicates work done by others (collected by Brent) who have gone much further, so this should just be considered an exercise of tools and techniques.  How to generate this form of numbers (b^n) in order of increasing size will be the subject of a future post.  We did not take advantage of algebraic factorization other than b^2-1 = (b+1)(b-1).

13^13-1 = [2, 2; 3, 1; 53, 1; 264031, 1
13^13+1 = [2, 1; 7, 1; 13417, 1; 20333, 1
13^14+1 = [2, 1; 5, 1; 17, 1
14^14+1 = [29, 2; 113, 1; 197, 1; 3361, 1
13^15-1 = [2, 2; 3, 2; 61, 1; 4651, 1; 30941, 1
13^15+1 = [2, 1; 7, 1; 11, 1; 31, 1; 157, 1; 2411, 1
14^15-1 = [11, 1; 13, 1; 31, 1; 211, 1; 2851, 1; 3761, 1
14^15+1 = [3, 2; 5, 2; 61, 1; 71, 1; 101, 1; 811, 1
15^15-1 = [2, 1; 7, 1; 11, 1; 61, 1; 241, 1; 4931, 1
15^15+1 = [2, 4; 31, 1; 211, 1; 1531, 1; 19231, 1
13^16+1 = [2, 1; 2657, 1; 441281, 1
14^16+1 = [193, 1
15^16+1 = [2, 1; 257, 1
13^17-1 = [2, 2; 3, 1; 103, 1; 443, 1
13^17+1 = [2, 1; 7, 1
14^17-1 = [13, 1; 103, 1
14^17+1 = [3, 1; 5, 1; 137, 1
15^17-1 = [2, 1; 7, 1; 1045002649, 1
15^17+1 = [2, 4; 137, 1; 443, 1
13^18+1 = [2, 1; 5, 1; 17, 1; 37, 1; 28393, 1; 428041, 1
14^18+1 = [37, 1; 197, 1; 1033, 1
17^17-1 = [2, 4; 10949, 1; 1749233, 1
17^17+1 = [2, 1; 3, 2
13^19-1 = [2, 2; 3, 1; 12865927, 1
13^19+1 = [2, 1; 7, 1
15^18+1 = [2, 1; 13, 1; 37, 1; 113, 1; 3877, 1
14^19-1 = [13, 1
14^19+1 = [3, 1; 5, 1; 191, 1; 26981, 1
17^18+1 = [2, 1; 5, 1; 29, 1; 37, 1; 109, 1; 181, 1; 2089, 1; 83233, 1
13^20+1 = [2, 1; 41, 1; 14281, 1; 29881, 1
15^19-1 = [2, 1; 7, 1; 4272113, 1
15^19+1 = [2, 4; 229, 1; 13757, 1
18^18+1 = [5, 2; 13, 1; 37, 2; 229, 1; 457, 1; 25309, 1
14^20+1 = [41, 1; 937, 1; 61001, 1; 698521, 1
17^19-1 = [2, 4; 229, 1; 1103, 1; 202607147, 1
17^19+1 = [2, 1; 3, 2; 457, 1; 1559, 1; 2927, 1; 312931, 1
13^21-1 = [2, 2; 3, 2; 43, 1; 61, 1; 337, 1; 547, 1; 2714377, 1
13^21+1 = [2, 1; 7, 2; 29, 1; 157, 1; 463, 1; 22079, 1
15^20+1 = [2, 1; 17, 1; 41, 1; 1201, 1; 1489, 1
18^19-1 = [17, 1; 6841, 1
18^19+1 = [19, 2
14^21-1 = [13, 1; 43, 1; 211, 1; 547, 1; 8108731, 1
14^21+1 = [3, 2; 5, 1; 61, 1; 463, 1; 7027567, 1
19^19-1 = [2, 1; 3, 2
19^19+1 = [2, 2; 5, 1; 108301, 1; 1049219, 1
13^22+1 = [2, 1; 5, 1; 17, 1; 5281, 1
17^20+1 = [2, 1; 41, 1; 41761, 1
15^21-1 = [2, 1; 7, 2; 43, 1; 241, 1; 1743463, 1
15^21+1 = [2, 4; 211, 1; 723031, 1; 10678711, 1
18^20+1 = [113, 1; 881, 1; 929, 1
14^22+1 = [197, 1; 88001, 1; 240159217, 1
19^20+1 = [2, 1; 17, 1; 41, 1; 3833, 1; 478382041, 1
13^23-1 = [2, 2; 3, 1; 1381, 1
13^23+1 = [2, 1; 7, 1; 47, 1; 277, 1; 1151, 1; 2347, 1
17^21-1 = [2, 4; 43, 1; 307, 1; 13567, 1; 25646167, 1
17^21+1 = [2, 1; 3, 3; 7, 2; 13, 1; 22796593, 1
15^22+1 = [2, 1; 113, 1; 617, 1
20^20+1 = [148721, 1; 160001, 1
18^21-1 = [7, 4; 17, 1; 449, 1; 80207, 1
18^21+1 = [19, 1; 43, 1; 307, 1; 46747, 1; 32222107, 1
14^23-1 = [13, 1; 47, 1; 461, 1; 2347, 1; 10627, 1; 2249861, 1
14^23+1 = [3, 1; 5, 1; 139, 1; 967, 1; 19922509, 1
13^24+1 = [2, 1; 1009, 1; 407865361, 1
19^21-1 = [2, 1; 3, 3; 127, 1; 701, 1; 70841, 1; 30640261, 1
19^21+1 = [2, 2; 5, 1; 7, 4; 43, 2; 197, 1; 226871, 1; 343393, 1
15^23-1 = [2, 1; 7, 1; 829, 1; 31741, 1
15^23+1 = [2, 4; 47, 1; 6257, 1; 81421, 1; 825287, 1
17^22+1 = [2, 1; 5, 1; 29, 1; 89, 1; 25741, 1; 256152733, 1
20^21-1 = [19, 1; 29, 1; 71, 1; 421, 1; 32719, 1; 460951, 1
20^21+1 = [3, 2; 7, 2; 43, 1; 127, 1; 827, 1; 10529, 1; 2750161, 1
14^24+1 = [17, 1; 5393, 1; 16097, 1; 19489, 1; 722833, 1
18^22+1 = [5, 2; 13, 1; 89, 1; 55547468813, 1
21^21-1 = [2, 2; 5, 1; 43, 1; 463, 1; 631, 1; 3319, 1; 4789, 1; 6427, 1
21^21+1 = [2, 1; 11, 1; 337, 1; 421, 1; 81867661, 1
13^25-1 = [2, 2; 3, 1; 701, 1; 9851, 1; 30941, 1
13^25+1 = [2, 1; 7, 1; 11, 1; 101, 1; 2411, 1; 57751, 1
19^22+1 = [2, 1; 181, 1; 774797, 1
15^24+1 = [2, 1; 3169, 1; 7121, 1; 179953, 1; 1659649, 1
17^23-1 = [2, 4; 47, 1
17^23+1 = [2, 1; 3, 2
20^22+1 = [89, 1; 401, 1; 170770770413, 1
14^25-1 = [11, 1; 13, 1; 3761, 1; 110256001, 1
14^25+1 = [3, 1; 5, 3; 71, 1; 101, 1; 401, 1; 4001, 1
18^23-1 = [17, 1; 47, 1; 599, 1; 7468009, 1
18^23+1 = [19, 1
13^26+1 = [2, 1; 5, 1; 17, 1; 380329, 1
21^22+1 = [2, 1; 13, 1; 17, 1; 89, 1; 661, 1
15^25-1 = [2, 1; 7, 1; 11, 1; 4931, 1; 46751, 1
15^25+1 = [2, 4; 31, 1; 1531, 1; 9555151, 1
19^23-1 = [2, 1; 3, 2; 277, 1; 2347, 1; 16497763013, 1
19^23+1 = [2, 2; 5, 1; 47, 1; 691, 1; 2531, 1
17^24+1 = [2, 1; 18913, 1; 184417, 1
22^22+1 = [5, 1; 97, 1; 9617835527609, 1
14^26+1 = [53, 1; 197, 1; 178616881, 1
20^23-1 = [19, 1; 691, 1; 1381, 1
20^23+1 = [3, 1; 7, 1; 47, 1; 461, 1; 563041, 1
13^27-1 = [2, 2; 3, 4; 61, 1; 650971, 1; 1609669, 1
13^27+1 = [2, 1; 7, 1; 19, 1; 157, 1; 163, 1; 271, 1; 937, 1; 904663, 1
18^24+1 = [97, 1; 1153, 1; 2474209, 1; 113607841, 1
21^23-1 = [2, 2; 5, 1; 47, 1; 19597, 1
21^23+1 = [2, 1; 11, 1; 277, 1; 461, 1; 599, 1; 691, 1
15^26+1 = [2, 1; 113, 1; 11909, 1; 16433, 1; 18617, 1; 30313817, 1
19^24+1 = [2, 1; 241, 1; 577, 1; 1009, 1; 4657, 1; 14929, 1; 15073, 1; 29569, 1
17^25-1 = [2, 4; 2551, 1; 5351, 1; 88741, 1; 26278001, 1
17^25+1 = [2, 1; 3, 2; 11, 1; 71, 1; 101, 1
22^23-1 = [3, 1; 7, 1; 4463, 1; 1323064018651, 1
22^23+1 = [23, 2; 47, 1; 461, 1; 1381, 1; 1933, 1
14^27-1 = [13, 1; 211, 1; 397, 1; 18973, 1; 1427145211, 1
14^27+1 = [3, 4; 5, 1; 19, 1; 61, 1; 132049, 1; 1177426963, 1
13^28+1 = [2, 1; 113, 1; 14281, 1
20^24+1 = [17, 1; 675796129, 1; 1505882353, 1
23^23-1 = [2, 1; 11, 1; 461, 1; 1289, 1; 831603031789, 1
23^23+1 = [2, 3; 3, 1; 47, 1; 139, 1; 1013, 1; 1641281, 1; 52626071, 1
18^25-1 = [17, 1; 41, 1; 2711, 1; 602401, 1
18^25+1 = [11, 1; 19, 1; 9041, 1; 738851, 1
21^24+1 = [2, 1; 193, 1; 433, 1; 673, 1; 62897, 1; 300673, 1; 1001713, 1
15^27-1 = [2, 1; 7, 1; 109, 1; 241, 1; 541, 1; 21061, 1; 16354441, 1
15^27+1 = [2, 4; 19, 1; 211, 1; 739, 1; 811, 1
19^25-1 = [2, 1; 3, 2; 101, 1; 151, 1; 911, 1; 1601, 1; 6451, 1
19^25+1 = [2, 2; 5, 3; 11, 1; 2251, 1; 79151, 1; 127051, 1
17^26+1 = [2, 1; 5, 1; 29, 1; 19825313, 1; 1224199237, 1
14^28+1 = [41, 1; 937, 1; 1009, 1; 774929, 1
22^24+1 = [17, 1; 241, 1; 940993, 1; 3227992561, 1
13^29-1 = [2, 2; 3, 1; 1973, 1; 2843, 1; 3539, 1
13^29+1 = [2, 1; 7, 1; 59, 1; 1741, 1; 8546789918171, 1
20^25-1 = [11, 1; 19, 1; 61, 1; 151, 1; 251, 1; 1451, 1; 1369801, 1; 7466201, 1
20^25+1 = [3, 1; 7, 1; 101, 1; 152381, 1
18^26+1 = [5, 2; 13, 2; 53, 1; 21997, 1; 5601346141, 1
23^24+1 = [2, 1; 17, 1; 3697, 1; 623009, 1; 12682129, 1
15^28+1 = [2, 1; 17, 1; 1489, 1; 766028506097, 1
21^25-1 = [2, 2; 5, 3; 40841, 1; 2031851, 1
21^25+1 = [2, 1; 11, 1; 101, 1; 185641, 1; 11093851, 1
24^24+1 = [17, 1; 2801, 1; 33409, 1; 2311681, 1; 13308961, 1
17^27-1 = [2, 4; 19, 1; 307, 1; 433, 1; 24733, 1; 1270657, 1
17^27+1 = [2, 1; 3, 5; 7, 1; 13, 1; 163, 1; 1423, 1; 5653, 1
14^29-1 = [13, 1; 13109, 1; 25581350023, 1
14^29+1 = [3, 1; 5, 1; 59, 1; 114221024581, 1
19^26+1 = [2, 1; 53, 1; 181, 1
13^30+1 = [2, 1; 5, 2; 17, 1; 421, 1; 601, 1; 641, 1; 28393, 1; 460655521, 1
22^25-1 = [3, 1; 7, 1; 245411, 1
22^25+1 = [23, 1; 101, 1; 154001, 1; 224071, 1; 727351, 1
20^26+1 = [53, 1; 401, 1; 502321, 1
18^27-1 = [7, 3; 17, 1; 991, 1; 23761, 1; 34327, 1; 253369, 1; 1464049, 1
18^27+1 = [19, 1; 73, 1; 307, 1; 465841, 1; 31865908033, 1
23^25-1 = [2, 1; 11, 1; 6551, 1; 292561, 1
23^25+1 = [2, 3; 3, 1; 31, 1; 41, 1; 101, 1; 211, 1; 56951, 1; 1068701, 1
15^29-1 = [2, 1; 7, 1; 59, 1
15^29+1 = [2, 4
21^26+1 = [2, 1; 13, 2; 17, 1; 53, 1; 32969, 1; 101089, 1
14^30+1 = [37, 1; 197, 1; 1033, 1; 1061, 1; 1383881, 1
17^28+1 = [2, 1; 2801, 1; 15121, 1; 41761, 1; 12876020081, 1
24^25-1 = [23, 1; 101, 1; 346201, 1; 1661037601, 1
24^25+1 = [5, 4; 11, 1; 151, 1; 5791, 1; 7951, 1; 86501, 1; 46739551, 1
19^27-1 = [2, 1; 3, 5; 127, 1; 487, 1; 523, 1; 29989, 1; 216919, 1; 907471, 1
19^27+1 = [2, 2; 5, 1; 7, 3; 199, 1; 41203, 1; 236377, 1; 2522827, 1
13^31-1 = [2, 2; 3, 1; 311, 1; 1117, 1
13^31+1 = [2, 1; 7, 1; 373, 1; 2729, 1; 145831193, 1
22^26+1 = [5, 1; 53, 1; 97, 1; 498733, 1; 2468996151857, 1
20^27-1 = [19, 1; 421, 1; 64008001, 1; 879338701, 1
20^27+1 = [3, 4; 7, 1; 109, 1; 127, 1; 307, 1; 4483, 1; 69481, 1; 99672121, 1
18^28+1 = [113, 1; 929, 1; 3697, 1
15^30+1 = [2, 1; 13, 1; 113, 1; 3877, 1; 19421, 1; 33601, 1; 131381, 1; 278041, 1
23^26+1 = [2, 1; 5, 1; 53, 1; 157, 1; 2861561, 1; 278640181, 1
14^31-1 = [13, 1
14^31+1 = [3, 1; 5, 1; 1613, 1; 3163, 1; 168269, 1; 7476844183, 1
13^32+1 = [2, 1; 193, 1; 1601, 1; 10433, 1
17^29-1 = [2, 4; 59, 1; 7193, 1; 6088087, 1
17^29+1 = [2, 1; 3, 2; 349, 1; 23549, 1; 2919779, 1; 18032534719, 1
21^27-1 = [2, 2; 5, 1; 109, 1; 163, 1; 463, 1; 4779433, 1; 85775383, 1
21^27+1 = [2, 1; 11, 1; 19, 1; 37, 1; 199, 1; 421, 1; 613, 1; 5077, 1; 17497, 1
19^28+1 = [2, 1; 17, 1; 3833, 1
24^26+1 = [577, 1; 20749, 1; 30030953107741, 1
22^27-1 = [3, 4; 7, 1; 13, 2; 109, 1; 127, 1; 163, 1; 433, 1; 297613, 1; 2558953, 1
22^27+1 = [19, 1; 23, 1; 463, 1; 3187, 1; 144667, 1; 1066231, 1; 5966803, 1
18^29-1 = [17, 1; 1505548068007783, 1
18^29+1 = [19, 1; 59, 1
20^28+1 = [617, 1; 1009, 1; 28393, 1; 160001, 1; 5417928377, 1
15^31-1 = [2, 1; 7, 1; 311, 1
15^31+1 = [2, 4; 958459, 1; 12871001296201, 1
14^32+1 = [7489, 1; 1204905857, 1; 1667461121, 1
13^33-1 = [2, 2; 3, 2; 23, 1; 61, 1; 419, 1; 859, 1; 18041, 1
13^33+1 = [2, 1; 7, 1; 67, 1; 157, 1; 331, 1; 1123, 1; 6997, 1; 122167, 1; 960961, 1
23^27-1 = [2, 1; 7, 1; 11, 1; 19, 1; 79, 1; 4591, 1; 7792003, 1; 15785281, 1
23^27+1 = [2, 3; 3, 4; 13, 2; 163, 1; 271, 1; 1117, 1
26^26+1 = [53, 1; 677, 1; 468363169, 1; 546547769, 1
17^30+1 = [2, 1; 5, 2; 29, 1; 61, 1; 541, 1; 21881, 1; 63541, 1; 83233, 1
21^28+1 = [2, 1; 617, 1; 97241, 1; 912521, 1; 115593326297, 1
19^29-1 = [2, 1; 3, 2; 59, 1; 233, 1; 297003021451861, 1
19^29+1 = [2, 2; 5, 1; 106373, 1; 670650007983077, 1
24^27-1 = [19, 1; 23, 1; 379, 1; 601, 1; 2017, 1; 2377, 1; 4987, 1; 2400571, 1
24^27+1 = [5, 2; 7, 1; 79, 1; 127, 1; 199, 1; 7561, 1
22^28+1 = [73, 1; 113, 1; 3209, 1; 3096409, 1
15^32+1 = [2, 1; 2689, 1; 1391359510721, 1
18^30+1 = [5, 3; 13, 1; 61, 1; 229, 1; 457, 1; 15101, 1; 15121, 1; 16921, 1; 145501, 1
20^29-1 = [19, 1; 59, 1; 929, 1; 10789, 1; 143609, 1; 466307299, 1
20^29+1 = [3, 1; 7, 1; 1741, 1; 10940140435272203, 1
14^33-1 = [13, 1; 67, 1; 211, 1; 4027, 1; 1154539, 1
14^33+1 = [3, 2; 5, 1; 23, 1; 61, 1; 424262851, 1; 11737870057, 1
13^34+1 = [2, 1; 5, 1; 17, 2; 1021, 1; 897329, 1; 61165661, 1; 75094577, 1
23^28+1 = [2, 1; 139921, 1
17^31-1 = [2, 4; 4093, 1; 6123493, 1
17^31+1 = [2, 1; 3, 2; 373, 1; 36845423, 1
26^27-1 = [5, 2; 19, 1; 37, 1; 109, 1; 433, 1; 308933353, 1; 7050697273, 1
26^27+1 = [3, 6; 7, 1; 31, 1; 1567, 1; 102966067, 1
21^29-1 = [2, 2; 5, 1; 59, 1; 1103704099, 1; 246763300513, 1
21^29+1 = [2, 1; 11, 1; 1277, 1
19^30+1 = [2, 1; 13, 2; 181, 1; 769, 1; 171434401, 1; 16936647121, 1
24^28+1 = [331777, 1; 8006209, 1
15^33-1 = [2, 1; 7, 1; 67, 1; 241, 1; 463, 1; 2333, 1; 8537, 1; 62475406423, 1
15^33+1 = [2, 4; 23, 1; 211, 1; 859, 1; 3055718821, 1; 23504771357, 1
18^31-1 = [17, 1; 311, 1; 12959, 1; 1276827537047, 1
18^31+1 = [19, 1; 1427, 1; 70619, 1
22^29-1 = [3, 1; 7, 1; 59, 1; 88987603, 1; 120593021, 1
22^29+1 = [23, 1; 428041, 1; 2283673499, 1; 15141642169, 1
14^34+1 = [197, 1; 2857, 1; 2774129, 1; 1253535423961, 1
13^35-1 = [2, 2; 3, 1; 211, 1; 30941, 1; 5229043, 1; 3357897971, 1
13^35+1 = [2, 1; 7, 2; 11, 1; 29, 1; 71, 1; 2411, 1; 22079, 1; 654221, 1; 759641, 1
20^30+1 = [13, 1; 41, 1; 401, 1; 2801, 1; 12277, 1; 71161, 1; 222361, 1; 55191001, 1
17^32+1 = [2, 1; 1409, 1; 165569, 1
23^29-1 = [2, 1; 11, 1; 233, 1; 1741, 1; 85087, 1; 11410109, 1
23^29+1 = [2, 3; 3, 1; 59, 1; 1075983677123, 1
26^28+1 = [17, 1; 113, 1; 26881, 1; 748217, 1; 16947835297, 1
19^31-1 = [2, 1; 3, 2
19^31+1 = [2, 2; 5, 1; 1503075053, 1; 14345411368517, 1
21^30+1 = [2, 1; 13, 1; 17, 1; 41, 1; 61, 1; 3181, 1; 1360861, 1; 920421641, 1
15^34+1 = [2, 1; 113, 1; 29173, 1; 712573, 1; 3395062589, 1
24^29-1 = [23, 1; 1973, 1; 10151, 1; 1130131, 1
24^29+1 = [5, 2; 59, 1; 1451, 1
13^36+1 = [2, 1; 73, 1; 4177, 1; 14281, 1; 181297, 1; 815702161, 1
14^35-1 = [11, 1; 13, 1; 3761, 1; 8108731, 1
14^35+1 = [3, 1; 5, 2; 71, 1; 101, 1; 2985431, 1; 7027567, 1
18^32+1 = [254209, 1; 475777, 1
22^30+1 = [5, 2; 97, 1; 157, 1; 181, 1; 401, 1; 1489, 1; 150901, 1; 468241, 1
20^31-1 = [19, 1; 311, 1; 11161, 1; 1646101, 1; 340037881769, 1
20^31+1 = [3, 1; 7, 1; 40487, 1; 75269, 1
28^28+1 = [449, 1; 23633, 1; 614657, 1; 54034289, 1; 213827041, 1
17^33-1 = [2, 4; 67, 1; 307, 1; 3697, 1; 976669, 1; 2141993519227, 1
17^33+1 = [2, 1; 3, 3; 7, 1; 13, 1; 23, 1; 199, 1; 947, 1; 991, 1; 48973, 1; 11372329, 1; 39172453, 1
23^30+1 = [2, 1; 5, 2; 37, 1; 53, 1; 61, 1; 941, 1; 7549, 1; 79561, 1; 272341, 1; 229533481, 1
19^32+1 = [2, 1; 151681, 1
21^31-1 = [2, 2; 5, 1; 4540713283, 1; 3936833990413, 1
21^31+1 = [2, 1; 11, 1; 78059, 1
26^29-1 = [5, 2; 59, 1
26^29+1 = [3, 3; 93878453, 1; 2593018849727, 1
15^35-1 = [2, 1; 7, 2; 11, 1; 71, 1; 4931, 1; 1743463, 1; 4167731, 1
15^35+1 = [2, 4; 31, 1; 1531, 1; 10678711, 1; 497638891, 1
13^37-1 = [2, 2; 3, 1; 1481, 1; 67495678093, 1; 4287755796749, 1
13^37+1 = [2, 1; 7, 1; 223, 1; 21017, 1; 152219, 1; 1548921490187, 1
14^36+1 = [41, 1; 73, 1; 937, 1; 1475750641, 1
24^30+1 = [13, 1; 61, 1; 73, 1; 349, 1; 577, 1; 182701, 1; 366001, 1; 1801385941, 1
18^33-1 = [7, 3; 17, 1; 23, 1; 199, 1; 16127, 1; 51217, 1
18^33+1 = [19, 1; 67, 1; 307, 1; 25939, 1; 536801, 1; 6301307, 1
22^31-1 = [3, 1; 7, 1; 3592159411, 1
22^31+1 = [23, 1; 373, 1; 24368768938283491, 1
20^32+1 = [193, 1; 577, 1; 641, 1
17^34+1 = [2, 1; 5, 1; 29, 1; 137, 1; 1361, 1; 2698649, 1; 1002402000793, 1
28^29-1 = [3, 3; 59, 1
28^29+1 = [29, 2; 40427, 1; 1074509, 1
19^33-1 = [2, 1; 3, 3; 67, 1; 127, 1; 2113, 1; 104281, 1; 34451077, 1; 62060021, 1
19^33+1 = [2, 2; 5, 1; 7, 3; 23, 1; 859, 1; 489061, 1; 519553, 1; 181258778383, 1
23^31-1 = [2, 1; 11, 1; 40888990028603, 1
23^31+1 = [2, 3; 3, 1; 8086847, 1; 2313675671730419, 1
21^32+1 = [2, 1
13^38+1 = [2, 1; 5, 1; 17, 1; 229, 1; 94621, 1
15^36+1 = [2, 1; 17, 1; 73, 1; 1489, 1; 24481, 1; 964764793, 1; 2562840001, 1
14^37-1 = [13, 1; 223, 1; 141405986837, 1
14^37+1 = [3, 1; 5, 1; 283051, 1; 118918748615980063, 1
29^29-1 = [2, 2; 7, 1; 59, 1; 16763, 1; 84449, 1; 2428577, 1; 14111459, 1; 58320973, 1
29^29+1 = [2, 1; 3, 1; 5, 1; 233, 1; 6864997, 1; 9487923853, 1
26^30+1 = [61, 1; 181, 1; 677, 1; 2521, 1; 170101, 1; 208518605101, 1
18^34+1 = [5, 2; 13, 1; 1429, 1; 6257, 1; 20786377, 1; 1292838509, 1
24^31-1 = [23, 1; 311, 1; 1613, 1; 9859, 1; 35279, 1; 39619, 1; 4045774723, 1
24^31+1 = [5, 2; 9289629982951807, 1
20^33-1 = [19, 1; 421, 1; 661, 1; 859, 1; 10778947368421, 1
20^33+1 = [3, 2; 7, 1; 23, 1; 67, 1; 127, 1; 38149, 1; 3049927, 1; 424016563147, 1
22^32+1 = [257, 1; 29571562823949828673, 1
17^35-1 = [2, 4; 88741, 1; 966211, 1; 21998621, 1; 25646167, 1
17^35+1 = [2, 1; 3, 2; 11, 1; 71, 1; 101, 1; 701, 1; 22796593, 1
28^30+1 = [5, 2; 13, 1; 61, 1; 157, 1; 1861, 1; 14561, 1; 45541, 1; 47221, 1; 84961, 1; 2449561, 1
13^39-1 = [2, 2; 3, 2; 53, 1; 61, 1; 79, 1; 1093, 1; 4603, 1; 21841, 1; 264031, 1; 1803647, 1
13^39+1 = [2, 1; 7, 1; 157, 1; 13417, 1; 20333, 1; 79301, 1
19^34+1 = [2, 1; 137, 2; 181, 1; 3084256577008769, 1
15^37-1 = [2, 1; 7, 1; 223, 1; 4441, 1; 32217011, 1; 2474070455887, 1
15^37+1 = [2, 4; 593, 1; 5928049943, 1
14^38+1 = [197, 1; 5363068468501, 1
23^32+1 = [2, 1; 257, 1
21^33-1 = [2, 2; 5, 1; 67, 1; 463, 1; 17513875027111, 1
21^33+1 = [2, 1; 11, 2; 23, 1; 421, 1; 3499, 1; 6073, 1; 28513, 1; 33199, 1; 10362529, 1
26^31-1 = [5, 2; 675574105122751103, 1
26^31+1 = [3, 3; 5147, 1; 15240792631413977, 1
29^30+1 = [2, 1; 37, 1; 61, 1; 313, 1; 421, 1; 541, 1; 1061, 1; 111855481, 1; 470925821, 1
18^35-1 = [17, 1; 41, 1; 71, 1; 449, 1; 2711, 1; 80207, 1; 4274201, 1
18^35+1 = [11, 1; 19, 1; 211, 1; 9041, 1; 117251, 1; 3052211, 1; 4179001, 1; 32222107, 1
24^32+1 = [449, 1; 12234999233, 1; 1377485825682881, 1
20^34+1 = [401, 1; 629433157137881, 1
17^36+1 = [2, 1; 73, 1; 1321, 1; 41761, 1; 72337, 1; 28639368230833, 1
22^33-1 = [3, 2; 7, 1; 13, 2; 67, 1; 353, 1; 121758187, 1; 1176469537, 1
22^33+1 = [23, 1; 89, 1; 463, 1; 9967, 1; 285451051007, 1
30^30+1 = [17, 1; 53, 1; 61, 1; 181, 1; 54121, 1; 421381, 1; 809101, 1; 4234801, 1; 12109381, 1
13^40+1 = [2, 1; 407865361, 1
15^38+1 = [2, 1; 113, 1; 26297, 1; 18434831466377, 1
14^39-1 = [13, 2; 157, 1; 211, 1; 761437, 1; 29914249171, 1
14^39+1 = [3, 2; 5, 1; 61, 1; 79, 1; 911, 1; 7307, 1; 40639, 1; 100621, 1
19^35-1 = [2, 1; 3, 2; 71, 1; 151, 1; 701, 1; 911, 1; 70841, 1
19^35+1 = [2, 2; 5, 2; 11, 1; 197, 1; 2251, 1; 226871, 1
28^31-1 = [3, 3; 10789, 1; 1675799, 1; 14307617, 1
28^31+1 = [29, 1; 1303, 1; 68690971367, 1
23^33-1 = [2, 1; 7, 1; 11, 2; 67, 1; 79, 1; 27919, 1; 23130823, 1; 3937230404603, 1
23^33+1 = [2, 3; 3, 2; 13, 2; 331, 1; 6073, 1; 39700406579747, 1
21^34+1 = [2, 1; 13, 1; 17, 2; 300293033, 1
18^36+1 = [113, 1; 929, 1; 11019855601, 1
26^32+1 = [128134849, 1; 1359389633857, 1
29^31-1 = [2, 2; 7, 1; 36767, 1; 15294622838198819, 1
29^31+1 = [2, 1; 3, 1; 5, 1; 3697433, 1; 192554086217, 1
17^37-1 = [2, 4; 149, 1; 223, 1; 1016919604559540581, 1
17^37+1 = [2, 1; 3, 2; 1481, 1; 2591, 1; 172683287783, 1
20^35-1 = [11, 1; 19, 1; 29, 1; 61, 1; 71, 1; 251, 1; 491, 1; 701, 1; 911, 1; 23311, 1; 32719, 1; 164011, 1
20^35+1 = [3, 1; 7, 2; 827, 1; 10529, 1; 17921, 1; 152381, 1; 7003781, 1; 31585261, 1
24^33-1 = [23, 1; 67, 1; 601, 1; 7349, 1; 134367047, 1; 690674662129, 1
24^33+1 = [5, 2; 7, 1; 79, 1; 991, 1; 9241, 1; 126127, 1; 60867245726761, 1
22^34+1 = [5, 1; 97, 1; 108461, 1
13^41-1 = [2, 2; 3, 1; 6740847065723, 1
13^41+1 = [2, 1; 7, 1; 83, 1; 638453, 1; 140299545168523469, 1
30^31-1 = [29, 1; 373, 1; 1085423538431, 1
30^31+1 = [31, 2; 4093, 1; 19469, 1; 48733, 1; 116189, 1; 139086132517, 1
14^40+1 = [17, 1; 4241, 1; 5393, 1; 16097, 1; 825039041, 1
15^39-1 = [2, 1; 7, 1; 53, 1; 241, 1; 1249, 1; 20749, 1; 157483, 1; 16655159, 1
15^39+1 = [2, 4; 79, 1; 211, 1; 5557501, 1; 1539711288259, 1
19^36+1 = [2, 1; 17, 1; 3833, 1; 4297, 1; 24841, 1; 3952393, 1
31^31-1 = [2, 1; 3, 1; 5, 1
31^31+1 = [2, 5; 373, 1; 1613, 1; 62869, 1; 145577, 1; 35789156484227, 1
21^35-1 = [2, 2; 5, 2; 43, 1; 631, 1; 1471, 1; 3319, 1; 40841, 1; 4149601, 1; 20028751, 1
21^35+1 = [2, 1; 11, 1; 71, 1; 140351, 1; 185641, 1; 78555121, 1; 81867661, 1
23^34+1 = [2, 1; 5, 1; 53, 1; 6121, 1; 246160726106632349, 1
28^32+1 = [7734913, 1; 13430849, 1; 2716827163186049, 1
18^37-1 = [17, 1; 157991, 1
18^37+1 = [19, 1; 1259, 1
26^33-1 = [5, 2; 19, 1; 23, 1; 37, 1; 67, 1; 65539, 1; 97395563, 1; 639024871, 1
26^33+1 = [3, 4; 7, 1; 31, 1; 16567, 1; 135938684703251, 1
17^38+1 = [2, 1; 5, 1; 29, 1; 247381, 1
13^42+1 = [2, 1; 5, 1; 17, 1; 673, 1; 2857, 1; 4621, 1; 28393, 1; 23161037562937, 1
29^32+1 = [2, 1; 193, 1; 63354497, 1
20^36+1 = [73, 1; 31177, 1; 160001, 1; 821113, 1; 4468393, 1
24^34+1 = [577, 1; 613, 1; 391273, 1; 7409898733, 1
22^35-1 = [3, 1; 7, 2; 245411, 1; 16968421, 1; 57036911, 1
22^35+1 = [23, 1; 29, 1; 43, 1; 71, 1; 86969, 1; 224071, 1; 882701, 1; 108635136821, 1
14^41-1 = [13, 1
14^41+1 = [3, 1; 5, 1; 83, 1; 5167, 1; 86501473, 1; 95263009, 1
15^40+1 = [2, 1; 1361, 1; 7121, 1; 179953, 1; 13535373521, 1
30^32+1 = Mat([185302018885184100000000000000000000000000000001, 1])
19^37-1 = [2, 1; 3, 2; 149, 1; 3588174588084451, 1
19^37+1 = [2, 2; 5, 1
21^36+1 = [2, 1; 73, 1; 97241, 1; 816769, 1; 518118697, 1; 808208209, 1
23^35-1 = [2, 1; 11, 1; 29, 1; 292561, 1; 5336717, 1; 15716677201, 1
23^35+1 = [2, 3; 3, 1; 31, 1; 41, 1; 71, 1; 211, 1; 673, 1; 2969, 1; 52291, 1; 12968551, 1; 6696671101, 1
18^38+1 = [5, 2; 13, 1; 60497, 1; 269117, 1; 74792209, 1; 6261053129, 1
31^32+1 = [2, 1; 4801, 1
28^33-1 = [3, 4; 199, 1; 271, 1; 6077039, 1; 50545507, 1
28^33+1 = [23, 2; 29, 1; 67, 1; 757, 1; 2377, 1; 365773, 1; 212170597, 1; 7351568071, 1
13^43-1 = [2, 2; 3, 1; 119627, 1
13^43+1 = [2, 1; 7, 1; 173, 1; 12566837, 1; 8001003293, 1; 346982008721, 1
17^39-1 = [2, 4; 157, 1; 307, 1; 212057, 1; 2919196853, 1
17^39+1 = [2, 1; 3, 3; 7, 1; 13, 2; 53, 1; 79, 1; 1249, 1; 65651, 1; 2001793, 1; 1837708051687, 1
26^34+1 = [677, 1; 83041563757, 1; 7702754097061, 1
14^42+1 = [29, 2; 37, 1; 113, 1; 197, 1; 1033, 1; 1597, 1; 3361, 1; 10333, 1; 176597, 1; 12471556693, 1
20^37-1 = [19, 1; 65269, 1; 2889957151, 1
20^37+1 = [3, 1; 7, 1; 149, 1; 368447, 1; 9609038940231949, 1
15^41-1 = [2, 1; 7, 1; 8430332222527, 1
15^41+1 = [2, 4; 83, 1
29^33-1 = [2, 2; 7, 1; 13, 1; 23, 1; 67, 1; 17607980281, 1; 18944890940537, 1
29^33+1 = [2, 1; 3, 2; 5, 1; 271, 1; 661, 1; 727, 1; 632743, 1; 5618383, 1; 72384467, 1; 163097089, 1
24^35-1 = [23, 1; 29, 1; 71, 1; 239, 1; 28771, 1; 346201, 1; 1892603411161, 1
24^35+1 = [5, 3; 11, 1; 5791, 1; 183458857, 1
22^36+1 = [73, 1; 2161, 1; 3209, 1; 191353, 1; 286777, 1; 514642753, 1
19^38+1 = [2, 1; 181, 1; 1217, 1
30^33-1 = [7, 2; 19, 1; 29, 1; 460087, 1; 5829525967, 1; 125673792020899, 1
30^33+1 = [13, 1; 23, 1; 31, 1; 67, 1; 397, 1; 88793, 1; 11275111, 1; 279811489, 1
21^37-1 = [2, 2; 5, 1; 31081, 1; 1681762703, 1
21^37+1 = [2, 1; 11, 1
18^39-1 = [7, 3; 17, 1; 79, 1; 521, 1; 7424759473, 1; 29759719289, 1
18^39+1 = [19, 1; 131, 1; 307, 1; 2081, 1; 4020180841, 1
13^44+1 = [2, 1; 89, 1; 6073, 1; 14281, 1
23^36+1 = [2, 1; 937, 1; 1153, 1; 139921, 1; 2968201, 1; 83575993, 1; 20521396873, 1
28^34+1 = [5, 1; 137, 1; 157, 1; 33049, 1
31^33-1 = [2, 1; 3, 2; 5, 1; 23, 1; 331, 1; 397, 1; 617, 1; 150332843, 1
31^33+1 = [2, 5; 7, 2; 19, 1; 67, 1; 297991, 1; 757241, 1; 1048563011, 1
17^40+1 = [2, 1; 241, 1; 18913, 1; 184417, 1; 3583912721, 1
14^43-1 = [13, 1; 173, 1
14^43+1 = [3, 1; 5, 1; 68138548314176704687, 1
15^42+1 = [2, 1; 13, 1; 29, 1; 113, 1; 3361, 1; 3877, 1; 327517, 1; 4454215139669, 1
20^38+1 = [401, 1; 362478049, 1; 2622927733, 1
26^35-1 = [5, 3; 11, 1; 8641, 1; 14561, 1; 321272407, 1; 9593937086651, 1
26^35+1 = [3, 3; 71, 2; 431, 1; 1021, 1; 2731, 1; 59011, 1
22^37-1 = [3, 1; 7, 1; 310727, 1; 1886989139768881, 1
22^37+1 = [23, 1; 149, 1; 2221, 1; 48397, 1; 9748223441962188353, 1
24^36+1 = [97, 1; 114769, 1; 331777, 1; 1134793633, 1
29^34+1 = [2, 1; 421, 1; 354553, 1
19^39-1 = [2, 1; 3, 3; 79, 1; 127, 1; 157, 1; 599, 1; 29251, 1; 133338869, 1; 887960971, 1
19^39+1 = [2, 2; 5, 1; 7, 3; 131, 1; 313, 1; 2341, 1; 176021, 1; 291331, 1
33^33-1 = [2, 5; 67, 1; 1123, 1; 2113, 1; 90619, 1; 91402147, 1; 747487377451, 1
33^33+1 = [2, 1; 7, 1; 17, 1; 23, 1; 151, 1; 661, 1; 1871, 1; 2705341, 1; 658526221, 1; 34544013769, 1
13^45-1 = [2, 2; 3, 3; 61, 1; 181, 1; 4651, 1; 30941, 1; 161971, 1; 1609669, 1
13^45+1 = [2, 1; 7, 1; 11, 1; 19, 1; 31, 1; 157, 1; 271, 1; 937, 1; 2251, 1; 2411, 1; 12601, 1; 28325071, 1
18^40+1 = [97, 1; 641, 1; 113607841, 1
30^34+1 = [17, 2; 53, 1; 137, 1; 8093, 1; 404569958213, 1; 1727160261481, 1
21^38+1 = [2, 1; 13, 1; 17, 1; 229, 1; 457, 1
23^37-1 = [2, 1; 11, 1; 1925658337781, 1
23^37+1 = [2, 3; 3, 1; 593, 1; 10445744467953088708693, 1
14^44+1 = [41, 1; 89, 1; 937, 1; 3697, 1; 2211409011924781241, 1
17^41-1 = [2, 4; 83, 1; 892079, 1; 13365673, 1; 960217114820653, 1
17^41+1 = [2, 1; 3, 2; 1231, 1; 62919257, 1; 18798033503, 1; 76203249126187, 1
15^43-1 = [2, 1; 7, 1
15^43+1 = [2, 4; 173, 1; 39205337, 1; 5519984993, 1; 16112471507273, 1
28^35-1 = [3, 3; 113, 1; 2521, 1; 206501, 1; 637421, 1; 4422461, 1
28^35+1 = [11, 1; 29, 1; 71, 1; 211, 1; 13007, 1; 35771, 1; 53951, 1; 59221, 1; 31384274881, 1
31^34+1 = [2, 1; 13, 1; 37, 1; 1399577, 1; 224499664484159761, 1
20^39-1 = [19, 1; 79, 1; 421, 1; 1171, 1; 3121, 1; 142559, 1; 9690539, 1
20^39+1 = [3, 2; 7, 1; 127, 1; 2081, 1; 2549, 1; 1340743, 1; 571945141, 1; 735408649, 1
26^36+1 = [17, 1; 73, 1; 26881, 1; 1586737, 1; 208826607601, 1; 2253596398489, 1
22^38+1 = [5, 1; 97, 1; 229, 1; 4789, 1; 654963203993173, 1
24^37-1 = [23, 1; 3701, 1; 48844975391, 1
24^37+1 = [5, 2; 149, 1; 724609, 1; 3487604250233977, 1
19^40+1 = [2, 1; 15073, 1; 563377, 1; 2772481, 1
29^35-1 = [2, 2; 7, 2; 71, 1; 732541, 1; 88009573, 1; 14222677166671, 1
29^35+1 = [2, 1; 3, 1; 5, 2; 11, 1; 31, 1; 281, 1; 401, 1; 141961, 1; 574995877, 1; 181767795581, 1
13^46+1 = [2, 1; 5, 1; 17, 1; 461, 1; 160081, 1; 159686609, 1; 1445443990517, 1
18^41-1 = [17, 1; 3811279, 1; 114341047, 1
18^41+1 = [19, 1; 83, 1; 168347, 1; 4354359491, 1; 24997711153, 1
21^39-1 = [2, 2; 5, 1; 79, 1; 463, 1; 547, 1; 1171, 1; 189437, 1; 516094151, 1
21^39+1 = [2, 1; 11, 1; 421, 1; 11701, 1; 629773, 1; 7021471715414521, 1
14^45-1 = [11, 1; 13, 1; 31, 1; 181, 1; 211, 1; 397, 1; 1171, 1; 2851, 1; 3761, 1; 15511, 1; 18973, 1; 302581, 1
14^45+1 = [3, 3; 5, 2; 19, 1; 61, 1; 71, 1; 101, 1; 811, 1; 132049, 1; 1948981, 1; 4020031, 1
33^34+1 = [2, 1; 5, 1; 109, 1; 130969, 1; 107201746410049, 1
17^42+1 = [2, 1; 5, 1; 29, 1; 1093, 1; 83233, 1; 5766433, 1; 100688449, 1
30^35-1 = [29, 1; 71, 1; 113, 1; 93997, 1; 167021, 1; 837931, 1; 1618891, 1; 73276901251, 1
30^35+1 = [11, 1; 31, 1; 631, 1; 44171, 1; 71261, 1; 1118041, 1; 1929481, 1; 1825230961, 1
23^38+1 = [2, 1; 5, 1; 53, 1; 761, 1; 1901, 1; 111236869, 1; 60848703597029, 1
15^44+1 = [2, 1; 17, 1; 89, 1; 1489, 1
20^40+1 = [17, 1; 76001, 1; 1505882353, 1; 32018865275041, 1
34^34+1 = [13, 1; 89, 1; 6009977, 1; 35794249, 1; 5397131237, 1
28^36+1 = [73, 1; 7129, 1; 7321, 1; 614657, 1; 51605161, 1; 343785529, 1
31^35-1 = [2, 1; 3, 1; 5, 2; 11, 1; 17351, 1; 319061, 1; 203633641, 1; 917087137, 1
31^35+1 = [2, 5; 41, 1; 71, 1; 11971, 1; 21821, 1; 71821, 1; 149269961, 1
26^37-1 = [5, 2; 1259, 1; 61504361, 1; 934196338628717, 1
26^37+1 = [3, 3; 149, 1; 223, 1; 64399463, 1
22^39-1 = [3, 2; 7, 1; 13, 3; 79, 1; 2003, 1; 1421317, 1; 85107437663, 1
22^39+1 = [23, 1; 463, 1; 1283881, 1; 21821513533, 1; 6165936796469347, 1
13^47-1 = [2, 2; 3, 1; 183959, 1; 19216136497, 1
13^47+1 = [2, 1; 7, 1; 498851139881, 1
19^41-1 = [2, 1; 3, 2; 10654507, 1; 11713456133, 1
19^41+1 = [2, 2; 5, 1; 83, 1; 3651133, 1
24^38+1 = [577, 1; 292753, 1; 22036657, 1
29^36+1 = [2, 1; 73, 1; 9001, 1; 353641, 1; 869689, 1; 55576681, 1
18^42+1 = [5, 2; 13, 1; 29, 1; 229, 1; 337, 1; 457, 1; 1373, 1; 17837, 1; 153133, 1; 1623833, 1; 31714369, 1
14^46+1 = [197, 1; 1381, 1; 7258585231384113470369, 1
21^40+1 = [2, 1; 241, 1; 9521, 1; 62897, 1; 300673, 1; 22995281, 1; 33534961, 1; 3184193681, 1
17^43-1 = [2, 4; 1549, 1; 3075877724153666279633, 1
17^43+1 = [2, 1; 3, 2; 8171, 1; 279119267104661, 1
15^45-1 = [2, 1; 7, 1; 11, 1; 61, 1; 181, 1; 241, 1; 541, 1; 4931, 1; 21061, 1; 39225301, 1
15^45+1 = [2, 4; 19, 1; 31, 1; 211, 1; 739, 1; 811, 1; 991, 1; 1531, 1; 19231, 1; 47701, 1; 142111, 1; 2568061, 1
23^39-1 = [2, 1; 7, 1; 11, 1; 79, 1; 47691619, 1; 480393499, 1
23^39+1 = [2, 3; 3, 2; 13, 3; 859, 1; 1489531614247, 1; 21001515080686141, 1
33^35-1 = [2, 5; 31, 1; 421, 1; 39451, 1; 3163483, 1
33^35+1 = [2, 1; 17, 1; 29, 1; 71, 1; 197, 1; 3571, 1; 219409, 1; 1151041, 1; 95688881, 1; 12364839691, 1
30^36+1 = [73, 1; 241, 1; 3361, 1; 13681, 1; 203309569, 1; 8987660137, 1; 154589869729, 1
20^41-1 = [19, 1; 739, 1; 788985829969499330639, 1
20^41+1 = [3, 1; 7, 1; 83, 1; 1723, 1; 824754607, 1; 35641617587, 1
13^48+1 = [2, 1; 97, 1; 2657, 1; 88993, 1; 441281, 1; 283763713, 1; 127028743393, 1
28^37-1 = [3, 3; 149, 1; 223, 1; 1481, 1; 20129, 1; 36129368689, 1
28^37+1 = [29, 1; 1004690609843, 1
34^35-1 = [3, 1; 11, 1; 61, 1; 463, 1; 631, 1; 6791, 1; 12251, 1; 18481, 1; 22571, 1; 3437617, 1
34^35+1 = [5, 2; 7, 2; 29, 1; 71, 1; 11131, 1; 104119, 1; 259631, 1
31^36+1 = [2, 1; 73, 1; 409, 1; 1129, 1; 4683817, 1; 852890113921, 1
22^40+1 = [17, 1; 3227992561, 1; 117040234821177281, 1
19^42+1 = [2, 1; 13, 2; 29, 1; 181, 1; 769, 1; 5237, 1; 2141413, 1; 1301151937, 1; 14533200697, 1
26^38+1 = [677, 1; 25841, 1; 546289, 1; 10675257997, 1; 317715361027301, 1
24^39-1 = [23, 1; 53, 1; 601, 1; 6553, 1; 15913, 1; 39313, 1; 6895253, 1
24^39+1 = [5, 2; 7, 1; 79, 1; 131, 1; 33203, 1; 76831, 1; 104911, 1; 304977817, 1
14^47-1 = [13, 1; 659, 1; 3690629, 1; 21156769, 1; 24572071, 1
14^47+1 = [3, 1; 5, 1; 1129, 1; 1693, 1; 273065677, 1
18^43-1 = [17, 1; 431, 1; 4464951753212028068412713, 1
18^43+1 = [19, 1; 5129762401, 1; 597455435179, 1
35^35-1 = [2, 1; 17, 1; 31, 1; 43, 1; 281, 1; 49831, 1; 6469961, 1; 44007727, 1; 6662221325761, 1
35^35+1 = [2, 2; 3, 2; 11, 1; 29, 1; 71, 1; 701, 1; 5209, 1; 11831, 1; 16661, 1; 132631, 1; 2358371, 1; 7601598131, 1
15^46+1 = [2, 1; 113, 1; 277, 1; 2393, 1; 488153, 1; 132653513, 1; 40193672100977, 1
29^37-1 = [2, 2; 7, 1; 149, 1; 13913, 1; 24603599107, 1
29^37+1 = [2, 1; 3, 1; 5, 1; 1259, 1; 9769, 1; 19085335524481, 1
17^44+1 = [2, 1; 353, 1; 41761, 1; 4578289, 1
21^41-1 = [2, 2; 5, 1; 83, 1; 14122861, 1; 83218931, 1; 17222085343, 1; 914531249431, 1
21^41+1 = [2, 1; 11, 1; 1231, 1; 1766117, 1
23^40+1 = [2, 1; 17, 1; 241, 1; 3697, 1; 623009, 1; 7249841, 1; 147190628299441, 1
13^49-1 = [2, 2; 3, 1; 1667, 1; 5229043, 1; 28082195177, 1
13^49+1 = [2, 1; 7, 3; 29, 1; 22079, 1; 435709, 1; 22896329, 1; 54461639, 1
20^42+1 = [13, 1; 197, 1; 401, 1; 12277, 1; 14561, 1; 1464961, 1; 8651161, 1; 1424354653, 1
30^37-1 = [29, 1; 149, 1; 223, 1
30^37+1 = [31, 1; 1259, 1; 9473, 1; 190181, 1; 197643419, 1; 223855477, 1
33^36+1 = [2, 1; 73, 1; 97, 1; 6113, 1; 15313, 1; 251857, 1; 91844017, 1
19^43-1 = [2, 1; 3, 2; 18917672548149688895557513, 1
19^43+1 = [2, 2; 5, 1; 2753, 1; 45597803, 1; 55578787747850091391, 1
28^38+1 = [5, 1; 157, 1; 10653073, 1; 4295845129, 1; 47560093775549, 1
14^48+1 = [97, 1; 193, 1; 37633, 1; 11284732320255809, 1
22^41-1 = [3, 1; 7, 1; 1298408911, 1; 91902256249183, 1
22^41+1 = [23, 1; 83, 1; 183594641609, 1
34^36+1 = [73, 1; 1336337, 1; 1785792568561, 1; 1062752044739689, 1
31^37-1 = [2, 1; 3, 1; 5, 1; 149, 1; 4219, 1; 152597832677, 1; 257803457371, 1; 386626708057, 1
31^37+1 = [2, 5; 969963587051157584202299, 1
26^39-1 = [5, 2; 19, 1; 37, 1; 79, 1; 313, 1; 27764777, 1; 3574533119, 1
26^39+1 = [3, 4; 7, 1; 31, 1; 547, 1; 859, 1; 937, 1; 6449, 1; 38299, 1; 397073, 1; 12562993, 1
24^40+1 = [17, 1; 2801, 1; 1252721, 1; 2311681, 1
18^44+1 = [113, 1; 929, 1; 21649, 1; 36309857, 1
15^47-1 = [2, 1; 7, 1; 283, 1; 659, 1; 2351, 1; 6299, 1; 183959, 1
15^47+1 = [2, 4; 2947920462206937499, 1
17^45-1 = [2, 4; 19, 1; 307, 1; 3691, 1; 33931, 1; 88741, 1; 316531, 1; 1270657, 1; 1674271, 1; 5113320301, 1
17^45+1 = [2, 1; 3, 4; 7, 1; 11, 1; 13, 1; 31, 1; 71, 1; 101, 1; 1423, 1; 5653, 1; 238212511, 1; 2220161311, 1
21^42+1 = [2, 1; 13, 1; 17, 1; 29, 1; 61, 1; 3181, 1; 3697, 1; 18481, 1; 68454248717, 1
29^38+1 = [2, 1; 421, 1
35^36+1 = [2, 1; 433, 1; 5737, 1; 9001, 1; 750313, 1; 392517673, 1; 2420496433, 1
13^50+1 = [2, 1; 5, 3; 17, 1; 421, 1; 601, 1; 641, 1; 1253653901, 1; 26771688828701, 1
23^41-1 = [2, 1; 11, 1; 83, 1; 117018989947, 1
23^41+1 = [2, 3; 3, 1; 1134389, 1; 44127446381, 1
20^43-1 = [19, 1; 369122321, 1
20^43+1 = [3, 1; 7, 1; 947, 1
30^38+1 = [17, 1; 53, 1; 229, 1; 12229313, 1; 14324887741, 1; 9359399031533, 1
14^49-1 = [13, 1; 491, 1; 50177, 1; 8108731, 1
14^49+1 = [3, 1; 5, 1; 7027567, 1; 1766644727, 1
33^37-1 = [2, 5; 149, 1; 223, 1; 678581, 1
33^37+1 = [2, 1; 17, 1; 6883, 1; 2030085143, 1; 22992024961, 1
19^44+1 = [2, 1; 17, 1; 89, 1; 3833, 1; 121434809, 1; 50766225049, 1; 18815582771569, 1
22^42+1 = [5, 1; 97, 1; 157, 1; 1489, 1; 3529, 1; 4481, 1; 83273, 1; 34379269, 1; 1267338829, 1
28^39-1 = [3, 4; 53, 1; 271, 1; 1483, 1; 1951, 1; 219386077, 1; 4543753614603737, 1
28^39+1 = [29, 1; 79, 1; 547, 1; 757, 1; 2237, 1; 114661, 1; 284467, 1; 1598039, 1
15^48+1 = [2, 1; 97, 1; 257, 1; 91297, 1; 12779004583099009, 1
18^45-1 = [7, 3; 17, 1; 31, 1; 41, 1; 601, 1; 991, 1; 2711, 1; 34327, 1; 558721, 1
18^45+1 = [11, 1; 19, 1; 73, 1; 307, 1; 9041, 1; 465841, 1; 828811, 1; 11630180251, 1
24^41-1 = [23, 1; 2789, 1; 40462534363, 1; 5079389540237737, 1
24^41+1 = [5, 2; 83, 1
26^40+1 = [241, 1; 401, 1; 3617, 1; 46559041, 1; 57734881, 1
17^46+1 = [2, 1; 5, 1; 29, 1; 1511845630837, 1
34^37-1 = [3, 1; 11, 1; 223, 1; 5107, 1; 38851, 1; 1157213, 1; 196591453916657, 1
34^37+1 = [5, 1; 7, 1; 3734683792412648487053, 1
31^38+1 = [2, 1; 13, 1; 37, 1; 1217, 1; 23126269, 1; 53489941, 1; 2491389137, 1
13^51-1 = [2, 2; 3, 2; 61, 1; 103, 1; 443, 1; 763879, 1; 15798461357509, 1
13^51+1 = [2, 1; 7, 1; 157, 1; 617886851384381281, 1
21^43-1 = [2, 2; 5, 1
21^43+1 = [2, 1; 11, 1; 173, 1; 15739, 1; 126851, 1; 169367548429, 1; 1163308526467, 1
29^39-1 = [2, 2; 7, 1; 13, 2; 67, 1; 521, 1; 148123, 1; 4748492087, 1
29^39+1 = [2, 1; 3, 2; 5, 1; 53, 1; 79, 1; 271, 1; 3407, 1; 7489, 1; 252918667, 1
35^37-1 = [2, 1; 17, 1; 388230138454493, 1; 1578885875119577, 1
35^37+1 = [2, 2; 3, 2; 149, 1; 1852073, 1; 2508617557697099, 1
23^42+1 = [2, 1; 5, 1; 37, 1; 53, 1; 7549, 1; 10781, 1; 598193, 1; 3250549, 1; 3391669, 1; 1707540478981, 1
20^44+1 = [34057, 1; 160001, 1; 40094590244240929, 1
14^50+1 = [197, 1; 1061, 1; 1383881, 1; 1289805301, 1
19^45-1 = [2, 1; 3, 4; 31, 1; 127, 1; 151, 1; 211, 1; 523, 1; 911, 1; 29989, 1; 584911, 1; 2460181, 1
19^45+1 = [2, 2; 5, 2; 7, 3; 11, 1; 61, 1; 199, 1; 271, 1; 2251, 1; 6661, 1; 236377, 1; 1081291, 1
30^39-1 = [7, 2; 19, 1; 29, 1; 157, 1; 911, 1; 13339, 1; 178907, 1; 252877, 1
30^39+1 = [13, 2; 31, 1; 67, 1; 79, 1; 547, 1; 184627, 1; 207169, 1; 4538397397, 1
15^49-1 = [2, 1; 7, 3; 1743463, 1; 5706541, 1; 10164071, 1; 4175288799599, 1
15^49+1 = [2, 4; 197, 1; 883471, 1; 10678711, 1; 25036159, 1; 35549599, 1; 93589065767, 1
33^38+1 = [2, 1; 5, 1; 109, 1
22^43-1 = [3, 1; 7, 1; 173, 1; 947, 1; 259799207, 1
22^43+1 = [23, 1
18^46+1 = [5, 2; 13, 1; 1381, 1; 415381, 1; 25753561, 1; 5184266309231761249, 1
17^47-1 = [2, 4
17^47+1 = [2, 1; 3, 2
28^40+1 = [17, 1; 241, 1; 15601, 1; 22223646961, 1; 4411542432420060881, 1
13^52+1 = [2, 1; 14281, 1; 86113, 1; 2176307537, 1; 224277684782113, 1
24^42+1 = [13, 1; 73, 1; 349, 1; 577, 1; 97238233, 1; 374925097, 1; 22165394411334301, 1
26^41-1 = [5, 2; 83, 1; 2633923, 1
26^41+1 = [3, 3; 9677, 1; 1532581, 1
37^37-1 = [2, 2; 3, 2; 149, 1; 1999, 1; 7993, 1; 16651, 1; 17317, 1; 10192715656759, 1
37^37+1 = [2, 1; 19, 1; 593, 1; 134135213, 1; 4356032201, 1; 6190006021, 1
31^39-1 = [2, 1; 3, 2; 5, 1; 79, 2; 331, 1; 13807, 1; 39703, 1; 42407, 1; 2426789, 1; 7908811, 1
31^39+1 = [2, 5; 7, 2; 19, 1; 157, 1; 17863, 1; 238213, 1; 42716694944587, 1
21^44+1 = [2, 1; 353, 1; 97241, 1; 313433209, 1; 715521049, 1; 29831330140869137, 1
34^38+1 = [13, 1; 89, 1; 229, 1; 457, 1; 19457, 1; 21972009770377241, 1
14^51-1 = [13, 1; 103, 1; 211, 1; 136273, 1; 22771730193675277, 1
14^51+1 = [3, 2; 5, 1; 61, 1; 137, 1; 379033, 1; 373751461, 1; 91949452849, 1; 390025544803, 1
29^40+1 = [2, 1; 17, 1; 26209, 1; 561377, 1; 1056241, 1; 128971441, 1; 4966942978351201, 1
20^45-1 = [11, 1; 19, 1; 31, 1; 61, 1; 251, 1; 421, 1; 3001, 1; 53101, 1; 261451, 1; 64008001, 1; 79083953101, 1
20^45+1 = [3, 3; 7, 1; 127, 1; 181, 1; 307, 1; 541, 1; 1621, 1; 54541, 1; 69481, 1; 152381, 1; 26876632021, 1
23^43-1 = [2, 1; 11, 1; 173, 1; 92107, 1
23^43+1 = [2, 3; 3, 1; 65542806503, 1
35^38+1 = [2, 1; 613, 1; 47881, 1; 301682835425375850779941, 1
15^50+1 = [2, 1; 101, 1; 113, 1; 1801, 1; 19421, 1; 115201, 1; 131381, 1
19^46+1 = [2, 1; 181, 1
18^47-1 = [17, 1; 20681, 1
18^47+1 = [19, 1; 468121, 1; 1286609209, 1
13^53-1 = [2, 2; 3, 1; 107, 1; 194723, 1; 189541180943969, 1; 8403659652641423, 1
13^53+1 = [2, 1; 7, 1; 3499, 1; 7504072417, 1; 202326783229, 1; 37379721025854083, 1
17^48+1 = [2, 1; 97, 1; 257, 1; 1120513, 1; 1801601, 1; 53160769, 1; 80592097, 1; 52548582913, 1
22^44+1 = [73, 1; 881, 1; 3209, 1; 3697, 1; 11617, 1; 486817, 1; 465308273, 1; 2598415601, 1
30^40+1 = [337, 1; 401, 1; 4855073, 1; 589750143841, 1
33^39-1 = [2, 5; 859, 1; 1123, 1; 5586803, 1; 255333703, 1; 307870362047, 1; 2309756737861, 1
33^39+1 = [2, 1; 7, 1; 17, 1; 79, 1; 151, 1; 157, 1; 313, 1; 19709, 1; 5079673, 1; 3321744947, 1; 78911260819, 1
28^41-1 = [3, 3; 83, 1; 821, 1; 801469, 1; 32512427, 1
28^41+1 = [29, 1; 9048878843, 1; 164175956442953113, 1
24^43-1 = [23, 1; 431, 1; 59083, 1; 22609057, 1
24^43+1 = [5, 2; 173, 1; 3011, 1; 20641, 1
26^42+1 = [29, 1; 181, 1; 677, 1; 2521, 1; 4733, 1; 694230517093, 1; 95340546766204237, 1
21^45-1 = [2, 2; 5, 2; 211, 1; 463, 1; 9391, 1; 18181, 1; 40841, 1; 41489011, 1; 57815101, 1; 85775383, 1
21^45+1 = [2, 1; 11, 1; 19, 1; 31, 1; 37, 1; 199, 1; 421, 1; 613, 1; 2551, 1; 185641, 1; 501001, 1; 658261, 1
37^38+1 = [2, 1; 5, 1; 137, 1; 176549, 1; 50604949357520823437009, 1
14^52+1 = [41, 1; 937, 1; 1873, 1; 122929, 1; 24265055276489, 1
31^40+1 = [2, 1; 17, 1; 25085030513, 1; 136046551681, 1
34^39-1 = [3, 2; 11, 1; 397, 1; 11701, 1; 328837393, 1; 2458736461986831391, 1
34^39+1 = [5, 1; 7, 1; 79, 1; 1123, 1; 1483, 1; 572833, 1; 2009983, 1; 1153361613301, 1
20^46+1 = [401, 1; 6373576093, 1; 10725299405489, 1
23^44+1 = [2, 1; 89, 1; 139921, 1; 77686774927081, 1
29^41-1 = [2, 2; 7, 1; 83, 1; 2789, 1; 446983, 1; 248807517236987713, 1
29^41+1 = [2, 1; 3, 1; 5, 1; 20747, 1; 812129, 1; 1453369, 1; 5055629, 1; 3711544517, 1; 350069058439, 1
15^51-1 = [2, 1; 7, 1; 103, 1; 241, 1; 1123, 1; 1022449, 1; 3496561, 1; 1045002649, 1; 6734509609, 1
15^51+1 = [2, 4; 137, 1; 211, 1; 443, 1; 101462866544971, 1
38^38+1 = [5, 1; 17, 2; 202921, 1; 3019633, 1; 378783161873, 1; 16529116201857929, 1
19^47-1 = [2, 1; 3, 2
19^47+1 = [2, 2; 5, 1; 283, 1; 11093, 1; 13948811059, 1
13^54+1 = [2, 1; 5, 1; 17, 1; 37, 1; 109, 1; 28393, 1; 428041, 1; 1471069, 1; 16764949, 1; 4220430741361, 1
35^39-1 = [2, 1; 13, 2; 17, 1; 97, 1; 157, 1; 443, 1; 4759, 1; 3500252342029, 1; 7852391301419627, 1
35^39+1 = [2, 2; 3, 3; 79, 1; 397, 1; 937, 1; 1483, 1; 22543, 1; 19073890993, 1; 248827600204171, 1
18^48+1 = [193, 1; 3930785153, 1; 30894471809, 1; 41448704449, 1
17^49-1 = [2, 4; 491, 1; 883, 1; 25646167, 1; 474969439337, 1; 1094794793219, 1
17^49+1 = [2, 1; 3, 2; 22796593, 1; 711954517, 1; 1465198716273377, 1
22^45-1 = [3, 3; 7, 1; 13, 2; 61, 1; 127, 1; 13591, 1; 245411, 1; 297613, 1; 396091, 1; 858794191, 1
22^45+1 = [19, 1; 23, 1; 31, 1; 463, 1; 631, 1; 19801, 1; 224071, 1; 2581921, 1; 5966803, 1; 1850478481, 1
30^41-1 = [29, 1; 83, 1; 2946343, 1; 3012431131, 1
30^41+1 = [31, 1; 2789, 1
24^44+1 = [89, 1; 5897, 1; 168433, 1; 331777, 1; 10720347881, 1
33^40+1 = [2, 1; 241, 1; 401, 1; 1251100321, 1; 703204309121, 1
14^53-1 = [13, 1; 107, 1; 24593, 1; 108342165348412451, 1; 212253211670183419, 1
14^53+1 = [3, 1; 5, 1
28^42+1 = [5, 1; 13, 1; 157, 1; 281, 1; 47221, 1; 93913, 1; 749729, 1; 1100860153, 1; 40860961267393, 1
21^46+1 = [2, 1; 13, 1; 17, 1; 477045301, 1; 11918195405621, 1
26^43-1 = [5, 2
26^43+1 = [3, 3; 681293, 1
31^41-1 = [2, 1; 3, 1; 5, 1; 83, 1; 42481797154433176612759, 1
31^41+1 = [2, 5; 7066933486329661873, 1
20^47-1 = [19, 1; 1129, 1; 4889, 1; 790551835729, 1; 1930941642781, 1
20^47+1 = [3, 1; 7, 1; 6863, 1; 64109, 1
15^52+1 = [2, 1; 17, 1; 1489, 1; 786553, 1; 14685091347707873, 1
37^39-1 = [2, 2; 3, 3; 7, 1; 67, 1; 157, 1; 16381, 1; 1414921, 1; 6765811783780036261, 1
37^39+1 = [2, 1; 19, 1; 31, 1; 43, 1; 53, 1; 79, 1; 591163, 1; 29991391, 1; 204576480239, 1
34^40+1 = [47441, 1; 74161, 1; 37642417, 1; 146030641, 1; 81428485012798241, 1
13^55-1 = [2, 2; 3, 1; 23, 1; 419, 1; 859, 1; 2861, 1; 18041, 1; 30941, 1; 13545148572117361, 1
13^55+1 = [2, 1; 7, 1; 11, 2; 2411, 1; 53681, 1; 128011456717, 1; 4122652482568228291, 1
23^45-1 = [2, 1; 7, 1; 11, 1; 19, 1; 79, 1; 292561, 1; 7792003, 1; 74912328481, 1
23^45+1 = [2, 3; 3, 3; 13, 2; 31, 1; 41, 1; 151, 1; 163, 1; 211, 1; 271, 1; 1117, 1; 189901, 1; 541119751, 1; 35799017131, 1
19^48+1 = [2, 1; 97, 1; 1486811410142377153, 1
29^42+1 = [2, 1; 37, 1; 61, 1; 313, 1; 421, 1; 2989309, 1; 427822081, 1; 826031641, 1; 45517753174237, 1
18^49-1 = [17, 1; 449, 1; 80207, 1; 101921, 1; 32401295018849, 1
18^49+1 = [19, 1; 883, 1; 29009, 1; 170227, 1; 32222107, 1; 86651455669280587, 1
17^50+1 = [2, 1; 5, 3; 29, 1; 5801, 1; 21881, 1; 63541, 1; 88301, 1; 373207301, 1
38^39-1 = [37, 1; 79, 1; 443, 1; 1483, 1; 7411, 1; 4967367318343, 1; 266044456723943, 1
38^39+1 = [3, 2; 7, 1; 13, 2; 53, 1; 67, 1; 547, 1; 368369, 1; 13664353, 1; 63625693, 1; 169450120009, 1
22^46+1 = [5, 1; 97, 1; 1013, 1; 52961256859009, 1; 913037865796506522713, 1
35^40+1 = [2, 1; 113, 1; 449, 1; 4481, 1; 22191649, 1; 3930254561, 1; 20020167221441, 1
14^54+1 = [37, 1; 109, 1; 197, 1; 1033, 1; 1297, 1; 56693904845761, 1
30^42+1 = [17, 1; 53, 1; 572573, 1; 809101, 1; 3466009, 1; 927132724337, 1; 78825757964689, 1
39^39-1 = [2, 1; 7, 1; 19, 1; 131, 1; 157, 1; 223, 1; 3121, 1; 8379073, 1; 617853265920983, 1
39^39+1 = [2, 3; 5, 1; 79, 1; 1483, 1; 30650569, 1; 1112201325769, 1; 58383427946248159, 1
24^45-1 = [19, 1; 23, 1; 241, 1; 601, 1; 2017, 1; 4987, 1; 17881, 1; 24481, 1; 346201, 1
24^45+1 = [5, 3; 7, 1; 11, 1; 31, 1; 79, 1; 127, 1; 199, 1; 271, 1; 3391, 1; 5791, 1; 7561, 1; 1090681, 1; 610250671, 1
21^47-1 = [2, 2; 5, 1; 49727, 1; 227011, 1; 75042551, 1; 158545759, 1; 5298873343, 1
21^47+1 = [2, 1; 11, 1; 283, 1; 1129, 1; 10165349, 1; 32036611, 1; 230199028303, 1
28^43-1 = [3, 3; 3613, 1; 60029, 1; 684217, 1; 105942074311, 1; 23321405465263, 1
28^43+1 = [29, 1; 5849, 1; 24385817, 1
26^44+1 = [17, 1; 89, 1; 26881, 1; 240769, 1; 262153, 1; 2383015361, 1; 12295864997249593, 1
33^41-1 = [2, 5; 83, 1; 2543, 1
33^41+1 = [2, 1; 17, 1; 665804387768740238351, 1
15^53-1 = [2, 1; 7, 1; 4423381, 1; 19273082604001, 1; 69249662260776479, 1
15^53+1 = [2, 4; 107, 1; 6618762113, 1; 80469189271, 1; 144923043227, 1
13^56+1 = [2, 1; 407865361, 1; 17254637799169, 1
20^48+1 = [97, 1; 10369, 1; 6756288659793814433, 1
31^42+1 = [2, 1; 13, 1; 29, 1; 37, 1; 7253, 1; 13469, 1; 922561, 1; 163598989, 1; 277739477, 1; 4038949965541, 1
23^46+1 = [2, 1; 5, 1; 53, 1; 428353, 1; 43166461432817, 1; 212620343166625553, 1
19^49-1 = [2, 1; 3, 2; 701, 1; 70841, 1; 167291881, 1; 51326794793, 1
19^49+1 = [2, 2; 5, 1; 197, 1; 226871, 1
37^40+1 = [2, 1; 17, 1; 103308219233, 1; 809300384771692001, 1
17^51-1 = [2, 4; 103, 1; 307, 1; 409, 1; 10949, 1; 1749233, 1; 2699538733, 1; 162260934541944127, 1
17^51+1 = [2, 1; 3, 3; 7, 1; 13, 1; 17341, 1; 14055956389, 1; 45628367677, 1; 225388217073157, 1
18^50+1 = [5, 4; 13, 1; 101, 1; 401, 1; 1201, 1; 15101, 1; 18401, 1; 102701, 1; 145501, 1; 1437058645425001, 1
34^41-1 = [3, 1; 11, 1; 57353507, 1
34^41+1 = [5, 1; 7, 1; 83, 1; 3553061, 1; 8077247, 1; 743440373206297391437, 1
29^43-1 = [2, 2; 7, 1; 173, 1; 13933, 1; 213633547, 1
29^43+1 = [2, 1; 3, 1; 5, 1; 1137465695629, 1; 2027049776208383967809, 1
14^55-1 = [11, 2; 13, 1; 67, 1; 3761, 1; 4027, 1; 1154539, 1
14^55+1 = [3, 1; 5, 2; 23, 1; 71, 1; 101, 1; 4193531, 1; 11737870057, 1; 80771150936583581, 1
22^47-1 = [3, 1; 7, 1; 24643699, 1; 40597567, 1; 10804373165265881, 1
22^47+1 = [23, 1; 195709, 1; 85735897693, 1
38^40+1 = [91921, 1; 539089, 1; 8065073, 1; 9541056283305131201, 1
35^41-1 = [2, 1; 17, 1; 821, 1; 12301, 1; 944969, 1; 16350253851226236901, 1
35^41+1 = [2, 2; 3, 2; 83, 1; 2531778485007234865183, 1
21^48+1 = [2, 1; 97, 1; 1217, 1; 2689, 1; 31873, 1; 6857635489, 1; 93310250563834657, 1
24^46+1 = [577, 1; 57162680989, 1
13^57-1 = [2, 2; 3, 2; 61, 1; 12865927, 1; 796956375829, 1; 9468940004449, 1
13^57+1 = [2, 1; 7, 1; 157, 1; 845083, 1; 2657518772948983, 1; 6061387217546931661, 1
15^54+1 = [2, 1; 13, 1; 37, 1; 113, 1; 3877, 1; 284329009, 1; 2560392206677, 1; 3506657472973, 1
30^43-1 = [29, 1; 947, 1; 1291, 1; 10704969713, 1; 638061101267, 1; 86600623517971, 1
30^43+1 = [31, 1; 33187577337197705392824941, 1
39^40+1 = [2, 1; 17, 1; 1361, 1; 3457, 1; 49121, 1; 17954081, 1; 45534289, 1
26^45-1 = [5, 3; 11, 1; 19, 1; 37, 1; 3061, 1; 8641, 1; 8821, 1; 9661, 1; 20785291, 1; 308933353, 1
26^45+1 = [3, 5; 7, 1; 31, 1; 431, 1; 1021, 1; 3691, 1; 102966067, 1; 216846518851, 1
28^44+1 = [89, 1; 614657, 1; 59716358541760548549065761, 1
20^49-1 = [19, 1; 29, 1; 71, 1; 32719, 1; 269737651, 1; 2488859795549, 1
20^49+1 = [3, 1; 7, 3; 827, 1; 10529, 1
33^42+1 = [2, 1; 5, 1; 13, 1; 109, 1; 91141, 1; 77899333, 1; 5928274539013, 1; 6029358788322409, 1
19^50+1 = [2, 1; 181, 1; 16936647121, 1; 675303194549101, 1; 590165627314172101, 1
17^52+1 = [2, 1; 41761, 1; 62507849, 1; 558796871153, 1; 1175496327058885417, 1
23^47-1 = [2, 1; 11, 1; 1612759, 1; 160782278895061740375167119, 1
23^47+1 = [2, 3; 3, 1; 908113047764652133, 1
18^51-1 = [7, 3; 17, 2; 103, 1; 10413571416962911, 1; 7563707819165039903, 1
18^51+1 = [19, 1; 137, 1; 307, 1; 443, 1; 133417, 1; 28281862627, 1; 1895634885375961, 1
40^40+1 = [17, 2; 113, 1; 337, 1; 641, 1; 929, 1; 14401, 1; 30241, 1; 3480641, 1
31^43-1 = [2, 1; 3, 1; 5, 1; 146982701137, 1
31^43+1 = [2, 5; 173, 1
14^56+1 = [17, 1; 5393, 1; 8737, 1; 16097, 1; 112639810230529, 1
37^41-1 = [2, 2; 3, 2; 83, 1; 739, 1; 2953, 1; 28123899653, 1
37^41+1 = [2, 1; 19, 1; 821, 1; 58331861039, 1; 501452405702859749917, 1
34^42+1 = [13, 1; 89, 1; 281, 1; 1069, 1; 1249, 1; 3613, 1; 539732593, 1; 122230011037, 1; 23913606373357, 1
29^44+1 = [2, 1; 89, 1; 353, 1; 617, 1; 353641, 1; 1521741545017, 1
22^48+1 = [449, 1; 174337, 1; 2310689, 1; 2902518892577, 1
13^58+1 = [2, 1; 5, 1; 17, 1; 233, 1; 20970714732554798304809, 1
15^55-1 = [2, 1; 7, 1; 11, 2; 67, 1; 463, 1; 2333, 1; 4931, 1; 8537, 1; 1011671, 1
15^55+1 = [2, 4; 23, 1; 31, 1; 331, 1; 1531, 1; 23504771357, 1; 3438685189501, 1; 58925748316711, 1
38^41-1 = [37, 1; 83, 1; 25913, 1; 142189, 1; 22323209900233969, 1
38^41+1 = [3, 1; 13, 1; 6788863, 1; 246440005795303973025847, 1
21^49-1 = [2, 2; 5, 1; 43, 1; 631, 1; 3319, 1; 7057, 1; 1606344741163, 1; 1767442850839, 1
21^49+1 = [2, 1; 11, 1; 81867661, 1; 2524084462789, 1; 86494371600108393937, 1
35^42+1 = [2, 1; 277, 1; 613, 1; 1597, 1; 5413, 1; 305369, 1; 11056997307329, 1
24^47-1 = [23, 1; 14759, 1; 497261, 1
24^47+1 = [5, 2; 659, 1; 22091, 1; 48198971, 1; 202112597, 1; 12844652726099, 1
30^44+1 = [89, 1; 241, 1; 3361, 1; 77155937, 1; 259715809, 1; 252778567915678303049, 1
20^50+1 = [41, 1; 401, 1; 2801, 1; 222361, 1
26^46+1 = [277, 1; 677, 1; 2393, 1; 9010481, 1; 6516608335877, 1
28^45-1 = [3, 5; 19, 2; 31, 1; 271, 1; 15991, 1; 444979, 1; 637421, 1; 734941, 1; 48403441, 1
28^45+1 = [11, 1; 29, 1; 37, 1; 127, 1; 757, 1; 1801, 1; 3061, 1; 3511, 1; 4621, 1; 53951, 1; 102547, 1; 691651, 1; 7302331, 1; 84673681, 1
17^53-1 = [2, 4; 4375997670680275555605273053, 1
17^53+1 = [2, 1; 3, 2; 107, 1; 33179, 1; 40992110362783761677, 1
19^51-1 = [2, 1; 3, 3; 103, 1; 127, 1; 307, 1; 613, 1; 3044803, 1; 54474019, 1; 99995282631947, 1
19^51+1 = [2, 2; 5, 1; 7, 3; 1531, 1; 1786596913, 1; 274019342889240109297, 1
39^41-1 = [2, 1; 19, 1; 2885417, 1; 3596683919, 1; 330870180284577457, 1
39^41+1 = [2, 3; 5, 1; 83, 1; 19294027, 1; 27943070272849883, 1
18^52+1 = [113, 1; 929, 1; 1873, 1; 260800658620746193, 1
33^43-1 = [2, 5; 6451, 1
33^43+1 = [2, 1; 17, 1; 173, 1; 947, 1; 545843, 1; 23964303573577, 1
14^57-1 = [13, 1; 211, 1; 229, 1; 428299, 1; 459715689149916492091, 1
14^57+1 = [3, 2; 5, 1; 61, 1; 191, 1; 26981, 1; 77312552100349, 1
23^48+1 = [2, 1; 97, 1; 193, 1; 2194369, 1; 229381734152257, 1; 15887591750468908417, 1
31^44+1 = [2, 1; 89, 1; 409, 1; 1129, 1; 414407390867564627396249, 1
40^41-1 = [3, 1; 13, 1; 83, 1; 474289, 1; 4280483, 1; 2361320821558176427807877, 1
40^41+1 = [41, 2; 2543, 1; 346369, 1; 123251070029752087, 1
13^59-1 = [2, 2; 3, 1; 273997, 1; 5311771, 1
13^59+1 = [2, 1; 7, 1; 5783, 1
22^49-1 = [3, 1; 7, 3; 51647, 1; 737353, 1; 16968421, 1; 1545133367, 1; 1987506739, 1
22^49+1 = [23, 1; 29, 1; 43, 1; 197, 1; 86969, 1; 58402513986319469, 1
29^45-1 = [2, 2; 7, 1; 13, 1; 67, 1; 181, 1; 14437, 1; 22111, 1; 41203, 1; 120691, 1; 732541, 1
29^45+1 = [2, 1; 3, 3; 5, 2; 11, 1; 19, 1; 31, 1; 271, 1; 401, 1; 32491, 1; 10435069, 1; 517475046481, 1
34^43-1 = [3, 1; 11, 1; 467927, 1; 2580689, 1; 2658042077, 1; 86102909407, 1
34^43+1 = [5, 1; 7, 1; 173, 1; 5419, 1; 105437, 1; 4599156088564925144271983, 1
15^56+1 = [2, 1; 2129, 1; 7121, 1; 66529, 1; 179953, 1; 198017, 1; 12515552561, 1; 1038405709913713, 1
37^42+1 = [2, 1; 5, 1; 13, 1; 29, 1; 137, 1; 337, 1; 673, 1; 144061, 1; 745529, 1; 452091109, 1; 8264338657, 1
21^50+1 = [2, 1; 13, 1; 17, 1; 41, 1; 19501, 1; 56501, 1; 920421641, 1; 33360993558601, 1
41^41-1 = [2, 3; 5, 1; 83, 1; 1752341, 1; 20567159, 1; 1876859311090803007, 1
41^41+1 = [2, 1; 3, 1; 7, 1; 18041, 1; 20396681, 1
24^48+1 = [193, 1; 349409, 1; 436417, 1; 2356609, 1; 76243169, 1; 13240554433, 1; 1216141647361, 1
38^42+1 = [5, 1; 17, 2; 8233, 1; 34273, 1; 1162253, 1; 2083693, 1; 946768313, 1
20^51-1 = [19, 1; 421, 1; 3061, 1; 60589, 1; 689852631578947368421, 1
20^51+1 = [3, 2; 7, 1; 103, 1; 127, 1; 409, 1; 1429, 1; 2567783, 1; 2640509, 1; 3698623, 1; 92054423, 1
35^43-1 = [2, 1; 17, 1; 964493527, 1; 6320945927587, 1
35^43+1 = [2, 2; 3, 2; 173, 1; 5693287, 1; 14463699096545759, 1; 940698020515363183, 1
17^54+1 = [2, 1; 5, 1; 29, 1; 37, 1; 109, 1; 181, 1; 2089, 1; 83233, 1; 382069, 1; 1941733, 1; 861553369, 1; 39902245921, 1
30^45-1 = [7, 2; 19, 1; 29, 1; 1171, 1; 12211, 1; 837931, 1; 51941161, 1; 729027001, 1
30^45+1 = [11, 1; 13, 1; 31, 1; 37, 1; 67, 1; 163, 1; 271, 1; 4831, 1; 19801, 1; 71261, 1; 120871, 1; 341191, 1; 517831, 1
14^58+1 = [197, 1; 233, 1; 19145784457, 1
19^52+1 = [2, 1; 17, 1; 2393, 1; 3833, 1; 7177, 1; 69034016679735329, 1
26^47-1 = [5, 2; 11986390598948220127, 1
26^47+1 = [3, 3; 2678044679, 1
18^53-1 = [17, 1; 4239894319, 1
18^53+1 = [19, 1; 107, 1; 144828226935207572844491, 1
28^46+1 = [5, 1; 157, 1; 893413, 1; 6013890309283753610697077, 1
23^49-1 = [2, 1; 11, 1; 29, 1; 197, 1; 5336717, 1
23^49+1 = [2, 3; 3, 1; 71, 1; 673, 1; 2969, 1; 171913108319, 1; 14284335193633, 1; 1414566930063953, 1
33^44+1 = [2, 1; 89, 1; 97, 1; 6113, 1; 47609, 1
39^42+1 = [2, 1; 29, 1; 281, 1; 761, 1; 5153, 1; 2311921, 1; 372498337, 1; 294662850413, 1
13^60+1 = [2, 1; 41, 1; 4441, 1; 8161, 1; 14281, 1; 29881, 1; 217561, 1; 815702161, 1; 543124566401, 1
15^57-1 = [2, 1; 7, 1; 241, 1; 4272113, 1; 292582141, 1; 370649274902657, 1
15^57+1 = [2, 4; 211, 1; 229, 1; 4561, 1; 13757, 1; 611028193819, 1; 439799488353587, 1
31^45-1 = [2, 1; 3, 3; 5, 2; 11, 1; 271, 1; 331, 1; 2521, 1; 3637, 1; 17351, 1; 63901, 1; 81343, 1; 106291, 1; 327412201, 1
31^45+1 = [2, 5; 7, 2; 19, 1; 41, 1; 577, 1; 21821, 1; 1538083, 1; 2065411, 1; 880374069121, 1
22^50+1 = [5, 3; 97, 1; 181, 1; 401, 1; 150901, 1
29^46+1 = [2, 1; 421, 1; 829, 1; 675608716093, 1; 3429444597413, 1
40^42+1 = [29, 1; 61, 1; 1601, 1; 41941, 1; 53040821, 1; 10900346689, 1; 1231682529008460481, 1
34^44+1 = [3257, 1; 1336337, 1; 791754459642521, 1; 1732429451995903321, 1
37^43-1 = [2, 2; 3, 2; 99576393613, 1; 798246265376983, 1; 96390918207548052857, 1
37^43+1 = [2, 1; 19, 1; 173, 1; 1033, 1; 1055189557, 1; 633412840509556667989937, 1
21^51-1 = [2, 2; 5, 1; 463, 1; 38047, 1; 1502097124754084594737, 1
21^51+1 = [2, 1; 11, 1; 103, 1; 421, 1; 11969, 1; 114089969144083169, 1
14^59-1 = [13, 1; 28439, 1; 1139110880064821580931661, 1
14^59+1 = [3, 1; 5, 1; 13217, 1; 20297, 1; 26914480954937, 1; 4723062582866725519259, 1
24^49-1 = [23, 1; 29, 1; 197, 1; 239, 1; 28771, 1; 125931208613032365313, 1
24^49+1 = [5, 2; 183458857, 1; 41006447819, 1; 5010044015761, 1
20^52+1 = [937, 1; 160001, 1; 1961441, 1; 26916259659749909489, 1
17^55-1 = [2, 4; 88741, 1; 15357101, 1; 3332897591, 1; 2141993519227, 1; 962619789378941, 1
17^55+1 = [2, 1; 3, 2; 11, 2; 23, 1; 71, 1; 101, 1; 947, 1; 87415373, 1
41^42+1 = [2, 1; 13, 1; 29, 2; 109, 1; 337, 1; 1993, 1; 59473, 1; 114576514249, 1; 22550075621233982641, 1
19^53-1 = [2, 1; 3, 2; 107, 1; 323930821687153, 1; 2551089855701675251204783, 1
19^53+1 = [2, 2; 5, 1; 104095533511, 1; 210146007928707977384770009, 1
18^54+1 = [5, 2; 13, 1; 37, 2; 109, 1; 229, 1; 457, 1; 2593, 1; 25309, 1; 771877, 1; 3711529, 1; 8640109, 1; 33388093, 1; 126001657, 1
26^48+1 = [97, 1; 101377, 1; 232185409, 1; 430164069753779201, 1
38^43-1 = [37, 1; 860828009, 1; 2910147166183, 1; 88551864386911823, 1
38^43+1 = [3, 1; 13, 1; 173, 1; 1033, 1; 1721, 1; 5849, 1; 1941881, 1; 1057926185892349, 1
35^44+1 = [2, 1; 89, 1; 750313, 1; 347731913, 1; 5803652050704688841, 1
30^46+1 = [17, 1; 53, 1; 4969, 1; 178687921, 1; 19176222677, 1; 70443348543908273093, 1
13^61-1 = [2, 2; 3, 1; 4027, 1; 4759, 1; 7687, 1; 27817, 1; 92110001, 1; 4672993939, 1; 48401662036451, 1
13^61+1 = [2, 1; 7, 1; 6024266671, 1; 298681203493, 1; 1535617756259, 1
28^47-1 = [3, 3; 6299, 1; 24128861, 1; 21277176429749, 1; 3425165712672937943, 1
28^47+1 = [29, 1; 175323719489, 1; 1892292333735833, 1
23^50+1 = [2, 1; 5, 3; 53, 1; 61, 1; 941, 1; 19501, 1; 272341, 1; 346924525001, 1
42^42+1 = [5, 1; 353, 1; 673, 1; 4621, 1; 11257, 1; 1350553, 1; 17825893, 1; 1689250516969, 1; 60652423637401, 1
15^58+1 = [2, 1; 113, 1; 233, 1; 1074277, 1; 281589769, 1; 1240581007181, 1
33^45-1 = [2, 5; 31, 1; 37, 1; 1123, 1; 4951, 1; 39451, 1; 34905511, 1; 275465191, 1
33^45+1 = [2, 1; 7, 1; 17, 1; 19, 1; 151, 1; 181, 1; 307, 1; 83071, 1; 221401, 1; 1151041, 1; 891687885391, 1; 1448986704001, 1
39^43-1 = [2, 1; 19, 1; 177677, 1; 214820928823, 1
39^43+1 = [2, 3; 5, 1; 31649, 1; 89527, 1; 67838335323899526766423, 1
22^51-1 = [3, 2; 7, 1; 13, 2; 239, 1; 613, 1; 74729519, 1; 176634767651, 1; 29084130008763268099, 1
22^51+1 = [23, 1; 103, 1; 137, 1; 463, 1; 128000923, 1; 1594728827, 1; 12513453088956661, 1
31^46+1 = [2, 1; 13, 1; 37, 1; 829, 1; 1955865713101, 1; 23856848059764277, 1
29^47-1 = [2, 2; 7, 1; 283, 1; 659693, 1; 4440937, 1; 7823903, 1; 16200263293163, 1; 100338952626091, 1
29^47+1 = [2, 1; 3, 1; 5, 1; 3740457218863, 1; 1363173240112199, 1; 148295428997500951, 1
21^52+1 = [2, 1; 97241, 1
14^60+1 = [41, 1; 937, 1; 61001, 1; 698521, 1; 51111761, 1; 1475750641, 1; 59203797481, 1
40^43-1 = [3, 1; 13, 1; 476178733, 1; 18786714449, 1
40^43+1 = [41, 1; 173, 1; 1291, 1; 3011, 1; 15166961, 1
17^56+1 = [2, 1; 113, 1; 337, 1; 18913, 1; 184417, 1; 45694428193, 1; 50667635531043971329, 1
34^45-1 = [3, 3; 11, 1; 37, 1; 61, 1; 181, 1; 271, 1; 397, 1; 22571, 1; 77431, 1; 13917511, 1; 22385281, 1
34^45+1 = [5, 2; 7, 1; 19, 1; 31, 1; 109, 1; 1123, 1; 6661, 1; 259631, 1; 745903, 1; 59299046581, 1
20^53-1 = [19, 1; 593071, 1; 24540050076369381718561, 1
20^53+1 = [3, 1; 7, 1; 107, 1
37^44+1 = [2, 1; 89, 1; 10529, 1; 16849632889, 1; 267892220390609, 1
24^50+1 = [61, 1; 577, 1; 667380601, 1; 1801385941, 1
18^55-1 = [17, 1; 23, 1; 41, 1; 199, 1; 2711, 1; 16127, 1; 51217, 1; 50790191, 1; 125500908706801, 1
18^55+1 = [11, 2; 19, 1; 331, 2; 9041, 1; 536801, 1; 6301307, 1; 11502811, 1; 142022651, 1; 6749141521, 1
19^54+1 = [2, 1; 13, 2; 37, 1; 73, 1; 109, 1; 181, 1; 769, 1; 35533, 1; 211573, 1; 113596956031609377829, 1
13^62+1 = [2, 1; 5, 1; 17, 1; 1861, 1; 1178621, 1; 48534593, 1; 111109852618983753193, 1
26^49-1 = [5, 2; 321272407, 1; 8377245533576547517, 1
26^49+1 = [3, 3; 71, 2; 197, 1; 42337, 1; 59011, 1; 23368004867873, 1
41^43-1 = [2, 3; 5, 1; 947, 1
41^43+1 = [2, 1; 3, 1; 7, 1; 173, 1; 2700487, 1; 809742915767321, 1; 886585272539761175429, 1
15^59-1 = [2, 1; 7, 1; 298157610720691362563759, 1
15^59+1 = [2, 4; 7907, 1; 565322071603278863, 1
30^47-1 = [29, 1; 1129, 1; 2351, 1; 218363, 1; 994991, 1
30^47+1 = [31, 1; 283, 1; 2348386754555590051440283, 1
23^51-1 = [2, 1; 7, 1; 11, 1; 79, 1; 103, 1; 42331, 1; 62246266355102810647, 1
23^51+1 = [2, 3; 3, 2; 13, 2; 239, 1; 117539, 1; 6023203, 1; 209209825938101, 1
28^48+1 = [97, 1; 2012449, 1; 4338337, 1; 168542177, 1
35^45-1 = [2, 1; 13, 1; 17, 1; 19, 1; 31, 1; 97, 1; 271, 1; 421, 1; 1621, 1; 49831, 1; 96753079, 1; 651811141, 1; 5196169021, 1
35^45+1 = [2, 2; 3, 4; 11, 1; 397, 1; 2251, 1; 132631, 1; 612740917, 1; 1028947411, 1; 235554165829621, 1
38^44+1 = [41, 1; 89, 1; 50857, 1
42^43-1 = [41, 1; 13910243, 1; 3542371317981806123086359389, 1
42^43+1 = [43, 2; 1033, 1; 117563, 1; 216803431799147308608401, 1
22^52+1 = [73, 1; 937, 1; 3209, 1
33^46+1 = [2, 1; 5, 1; 109, 1; 277, 1; 56857, 1; 77557, 1; 944343455669, 1
14^61-1 = [13, 1; 977, 1; 8053, 1; 21961, 1; 51238644631619299, 1
14^61+1 = [3, 1; 5, 1; 90281, 1; 107705383, 1
39^44+1 = [2, 1; 1156721, 1; 2904529, 1
21^53-1 = [2, 2; 5, 1; 1697, 1; 207612155793974069, 1; 372515213872960388437, 1
21^53+1 = [2, 1; 11, 1; 107, 1; 8693, 1; 167223466685805761701453712891, 1
31^47-1 = [2, 1; 3, 1; 5, 1; 3128573142495569, 1; 170942984502845969696543, 1
31^47+1 = [2, 5; 659, 1; 20681, 1; 322825141, 1
17^57-1 = [2, 4; 229, 1; 307, 1; 1103, 1; 202607147, 1; 291973723, 1; 6162410920417, 1
17^57+1 = [2, 1; 3, 3; 7, 1; 13, 1; 457, 1; 1559, 1; 2927, 1; 312931, 1; 20352763, 1
13^63-1 = [2, 2; 3, 3; 43, 1; 61, 1; 127, 1; 337, 1; 547, 1; 6301, 1; 825679, 1; 1609669, 1; 2714377, 1; 5229043, 1; 7327657, 1; 997294663, 1
13^63+1 = [2, 1; 7, 2; 19, 1; 29, 1; 157, 1; 271, 1; 463, 1; 937, 1; 22079, 1; 11032183, 1; 704972647, 1; 54165939703, 1
29^48+1 = [2, 1; 97, 1; 125123236840173674393761, 1
43^43-1 = [2, 1; 3, 1; 7, 1; 173, 1; 120401, 1
43^43+1 = [2, 2; 11, 1; 947, 1; 1291, 1; 6709, 1; 86689, 1; 485926008972226664331036683, 1
20^54+1 = [13, 1; 37, 1; 401, 1; 7237, 1; 12277, 1; 24877, 1; 4450002049, 1
18^56+1 = [97, 1; 673, 1; 5105857, 1; 113607841, 1; 6139221193320769, 1
19^55-1 = [2, 1; 3, 2; 151, 1; 911, 1; 104281, 1; 62060021, 1; 484536191701, 1
19^55+1 = [2, 2; 5, 2; 11, 2; 23, 1; 2251, 1; 253239693257, 1; 150669382018464871, 1
24^51-1 = [23, 1; 307, 1; 601, 1; 1531, 1; 2347, 1; 120574031, 1; 6166060753, 1; 341563234253, 1
24^51+1 = [5, 2; 7, 1; 79, 1; 103, 1; 409, 1; 10133, 1; 36941239, 1; 1585038487, 1; 11144891198810483, 1
34^46+1 = [13, 1; 89, 1; 829, 1; 1617671053, 1; 186301449656789, 1; 7170136256368009, 1
40^44+1 = [769, 1; 881, 1; 3329, 1; 6073, 1; 6689, 1; 516209, 1; 4846608286096885634129, 1
15^60+1 = [2, 1; 17, 1; 41, 1; 1201, 1; 1489, 1; 17761, 1; 2414458561, 1; 2562840001, 1; 133390439104361, 1
37^45-1 = [2, 2; 3, 4; 7, 1; 11, 1; 41, 1; 67, 1; 73, 1; 127, 1; 2671, 1; 4021, 1; 4271, 1; 92251, 1; 318211, 1; 16133851, 1; 108998178168331, 1
37^45+1 = [2, 1; 19, 1; 31, 1; 43, 1; 181, 1; 199, 1; 601, 1; 1531, 1; 51031, 1; 1824841, 1; 12892843, 1; 6002229721, 1
26^50+1 = [101, 1; 601, 1; 677, 1; 208518605101, 1
23^52+1 = [2, 1; 313, 1; 139921, 1
30^48+1 = [97, 1; 257, 1; 105601, 1; 249352417, 1; 17940767041, 1; 69250296257, 1
28^49-1 = [3, 3; 113, 1; 197, 1; 2155609, 1; 4422461, 1; 319343666713, 1
28^49+1 = [29, 1; 13007, 1; 28813, 1; 35771, 1; 51647, 1; 57527, 1; 248397367, 1; 5966523512629, 1
41^44+1 = [2, 1; 89, 1; 137, 1; 10313, 1; 86857, 1; 218404913, 1; 5464786215794929, 1
35^46+1 = [2, 1; 613, 1; 1124576725295981, 1; 17881783852634882214225337, 1
14^62+1 = [197, 1; 446401, 1
38^45-1 = [11, 1; 31, 1; 37, 1; 109, 1; 151, 1; 163, 1; 181, 1; 1483, 1; 9871, 1; 91621, 1; 169471, 1; 194681, 1; 1649019241, 1
38^45+1 = [3, 3; 7, 1; 13, 1; 67, 1; 421, 1; 811, 1; 94111, 1; 112621, 1; 127261, 1; 2031671, 1; 1003627171, 1; 21471693391, 1
22^53-1 = [3, 1; 7, 1; 8432873783478996906159449, 1
22^53+1 = [23, 1; 107, 1; 180413, 1; 359129, 1; 3157235118397, 1
13^64+1 = [2, 1; 257, 1; 3230593, 1; 36713826768408543617, 1
17^58+1 = [2, 1; 5, 1; 29, 2; 4908077, 1
33^47-1 = [2, 5; 69412891, 1; 261473503, 1; 1100942133956936933797, 1
33^47+1 = [2, 1; 17, 1; 283, 1; 8179, 1
21^54+1 = [2, 1; 13, 1; 17, 1; 61, 1; 1693, 1; 3181, 1; 4344847859197, 1; 360697466924286697, 1
42^44+1 = [17, 1; 183041, 1; 154185769, 1
18^57-1 = [7, 3; 17, 1; 6841, 1; 1288363483639, 1; 6089884909802812423, 1
18^57+1 = [19, 2; 307, 1; 1961870762757168078553, 1
20^55-1 = [11, 2; 19, 1; 61, 1; 251, 1; 2209901, 1; 10778947368421, 1; 2571413672161047121, 1
20^55+1 = [3, 1; 7, 1; 23, 1; 152381, 1; 424016563147, 1
31^48+1 = [2, 1; 193, 1; 1889, 1; 7393, 1; 1347329, 1; 6139297, 1; 23277313, 1; 27333034608226177, 1
39^45-1 = [2, 1; 7, 1; 19, 1; 31, 1; 181, 1; 191, 1; 223, 1; 271, 1; 401, 1; 1741, 1; 31321, 1; 2461861, 1; 19440901, 1; 2995328101, 1
39^45+1 = [2, 3; 5, 2; 11, 1; 61, 1; 1171, 1; 1483, 1; 2089, 1; 5641, 1; 41011, 1; 1684387, 1; 13658401, 1; 15952141, 1; 25835671, 1
19^56+1 = [2, 1; 113, 1; 14561, 1; 15073, 1; 563377, 1; 38645462353, 1; 107849044129, 1
29^49-1 = [2, 2; 7, 3; 197, 1; 88009573, 1; 1458862987, 1
29^49+1 = [2, 1; 3, 1; 5, 1; 574995877, 1; 734893353967822492171, 1
15^61-1 = [2, 1; 7, 1; 367, 1; 7321, 1; 220692472927167836907173, 1
15^61+1 = [2, 4; 234519435023, 1; 1805790344137304843, 1
24^52+1 = [521, 1; 331777, 1; 64223630017, 1
43^44+1 = [2, 1; 17, 1; 89, 1; 193, 1; 521, 1; 2113, 1; 89849, 1; 267606343535521, 1; 489324727930193, 1
34^47-1 = [3, 1; 11, 1; 941, 1
34^47+1 = [5, 1; 7, 1; 8179, 1; 2572040051929, 1; 3070899174042608439765029, 1
40^45-1 = [3, 3; 13, 1; 31, 1; 163, 1; 547, 1; 2625641, 1; 8376409, 1; 206124513031, 1
40^45+1 = [7, 1; 11, 2; 19, 1; 37, 1; 41, 1; 223, 1; 379, 1; 15373, 1; 20641, 1; 6717334976041, 1; 336244505171718601, 1
37^46+1 = [2, 1; 5, 1; 137, 1; 277, 1; 461, 1; 54316709, 1
26^51-1 = [5, 2; 19, 1; 37, 1; 103, 1; 1123, 1; 216649, 1; 1696363, 1; 40385656825829055229, 1
26^51+1 = [3, 4; 7, 1; 31, 1; 1531, 1; 3299, 1; 4999, 1; 1935281, 1; 1315750871, 1
23^53-1 = [2, 1; 11, 1; 107, 1; 134515657106693, 1; 61190665486751483, 1
23^53+1 = [2, 3; 3, 1; 568952669, 1
14^63-1 = [13, 1; 43, 1; 211, 1; 379, 1; 397, 1; 547, 1; 18973, 1; 8108731, 1; 407364049, 1; 2239000891, 1
14^63+1 = [3, 3; 5, 1; 19, 1; 61, 1; 127, 1; 463, 1; 132049, 1; 7027567, 1; 131147620297, 1
44^44+1 = [41, 1; 113, 1; 353, 1; 809, 1; 9857, 1; 21889297, 1; 515247198207611779162177, 1
28^50+1 = [5, 3; 61, 1; 101, 1; 157, 1; 14561, 1; 84961, 1; 67643801, 1; 192184659301, 1; 360728480233546501, 1
30^49-1 = [29, 1; 71, 1; 113, 1; 93997, 1; 1984109, 1; 71761730340566743, 1
30^49+1 = [31, 1; 631, 1; 883, 1; 1118041, 1; 7373227, 1
13^65-1 = [2, 2; 3, 1; 53, 1; 131, 1; 1171, 1; 30941, 1; 156131, 1; 264031, 1; 1803647, 1; 71442881968439190301, 1
13^65+1 = [2, 1; 7, 1; 11, 1; 2411, 1; 13417, 1; 16381, 1; 20333, 1; 79301, 1; 3808876542352598861, 1
22^54+1 = [5, 1; 37, 1; 97, 1; 157, 1; 1489, 1; 18973, 1; 522289, 1; 25043041, 1; 5847988213, 1; 18311943313, 1
35^47-1 = [2, 1; 17, 1; 12503, 1; 17203, 1
35^47+1 = [2, 2; 3, 2; 6855123337, 1; 1169998714395426255963736661117, 1
41^45-1 = [2, 3; 5, 2; 31, 1; 271, 1; 487, 1; 811, 1; 1723, 1; 22381, 1; 579281, 1; 9753949, 1; 11228251, 1; 2355405711202441, 1
41^45+1 = [2, 1; 3, 3; 7, 1; 11, 1; 19, 1; 37, 1; 61, 1; 73, 1; 547, 1; 4111, 1; 30853, 1; 100697041, 1; 8179560752161, 1
17^59-1 = [2, 4; 1063, 1; 1889, 1; 1365581260423071390161, 1
17^59+1 = [2, 1; 3, 2; 512593, 1; 682807427588431379494344607469, 1
38^46+1 = [5, 1; 17, 2; 277, 1; 461, 1; 98873184304052969, 1
21^55-1 = [2, 2; 5, 2; 881, 1; 40841, 1; 5664205361, 1; 17513875027111, 1; 270573999780463721, 1
21^55+1 = [2, 1; 11, 2; 23, 1; 2971, 1; 6073, 1; 185641, 1; 10362529, 1; 8407123807237422961, 1
18^58+1 = [5, 2; 13, 1; 233, 1; 9049, 1; 23201, 1; 5860321, 1; 874663781, 1; 678538785553421893, 1
20^56+1 = [17, 1; 113, 1; 449, 1; 1505882353, 1
33^48+1 = [2, 1; 577, 1; 1153, 1; 165601, 1; 69789409, 1; 110720417, 1; 205779361, 1; 23363951137, 1; 15480661570849, 1
19^57-1 = [2, 1; 3, 3; 127, 1; 229, 1; 6841, 1; 80558460464029837, 1; 81403978301424181910737, 1
19^57+1 = [2, 2; 5, 1; 7, 3; 457, 1; 17443, 1; 108301, 1; 166783, 1; 1049219, 1; 870542161121, 1; 13983359177311, 1
15^62+1 = [2, 1; 113, 1; 20089, 1; 856469, 1; 18167443254760948901, 1
42^45-1 = [11, 1; 13, 1; 19, 1; 41, 1; 61, 1; 139, 1; 181, 1; 1601, 1; 518131, 1; 288900307, 1; 154954759291, 1; 23214437040060361, 1
42^45+1 = [31, 1; 43, 1; 131, 1; 1723, 1; 23201, 1; 45481, 1; 7030981, 1; 5488957657, 1; 27171831445741, 1
31^49-1 = [2, 1; 3, 1; 5, 1; 6959, 1; 917087137, 1
31^49+1 = [2, 5; 11971, 1; 71821, 1; 2932755253, 1
29^50+1 = [2, 1; 101, 1; 421, 1; 1061, 1; 4801, 1; 470925821, 1
24^53-1 = [23, 1
24^53+1 = [5, 2; 107, 1; 1061, 1; 450077, 1
39^46+1 = [2, 1; 761, 1; 3221, 1; 4049, 1; 5484150361, 1; 662961159337, 1
14^64+1 = [8633886977, 1
43^45-1 = [2, 1; 3, 3; 7, 1; 19, 1; 181, 1; 199, 1; 631, 1; 3079, 1; 6211, 1; 9001, 1; 3500201, 1; 11416525335601, 1
43^45+1 = [2, 2; 11, 1; 13, 1; 31, 1; 109, 1; 139, 1; 6481, 1; 3341101, 1; 33007141, 1; 57993427, 1; 59528191, 1; 13775424211, 1
34^48+1 = [97, 1; 257, 1; 375841, 1; 49805953, 1; 2583249857, 1; 23775511777, 1; 49521227489, 1; 3928666141537, 1
13^66+1 = [2, 1; 5, 1; 17, 1; 5281, 1; 28393, 1; 37869877, 1; 23057835113017, 1; 3577574298489429481, 1
23^54+1 = [2, 1; 5, 1; 37, 1; 53, 1; 73, 1; 109, 1; 757, 1; 4789, 1; 5689, 1; 7549, 1; 101089, 1; 1636741, 1; 18996553, 1
26^52+1 = [17, 1; 8737, 1; 26881, 1
40^46+1 = [1601, 1; 24841, 1
37^47-1 = [2, 2; 3, 2; 11939, 1; 169997350583, 1; 4004953934692253, 1
37^47+1 = [2, 1; 19, 1; 941, 1; 42677, 1; 2445622952400877178321483907583, 1
28^51-1 = [3, 4; 103, 1; 271, 1; 57427, 1; 8061059901399457, 1; 148020807352107352204781, 1
28^51+1 = [29, 1; 239, 1; 613, 1; 757, 1; 2347, 1; 8807, 1; 45508138747, 1
17^60+1 = [2, 1; 41, 1; 73, 1; 601, 1; 1321, 1; 41761, 1; 72337, 1; 73363561, 1; 1186844128302568601, 1
22^55-1 = [3, 1; 7, 1; 67, 1; 331, 1; 353, 1; 118361, 1; 245411, 1; 1176469537, 1
22^55+1 = [23, 1; 89, 1; 224071, 1; 2706385001, 1; 285451051007, 1; 1357357714241, 1
30^50+1 = [17, 1; 53, 1; 1801, 1; 54121, 1; 12109381, 1; 39974961601, 1; 2441218904701, 1
44^45-1 = [7, 1; 19, 1; 37, 1; 43, 1; 181, 1; 271, 1; 283, 1; 391801, 1; 2062891, 1; 3835261, 1; 10322047, 1; 35041021, 1; 107890772359411, 1
44^45+1 = [3, 4; 5, 2; 31, 1; 421, 1; 631, 1; 1621, 1; 1741, 1; 15139, 1; 159769, 1; 413521, 1; 1120771, 1
21^56+1 = [2, 1; 113, 1; 12097, 1; 62897, 1; 300673, 1; 31548272195219921, 1
18^59-1 = [17, 1; 4295428888967, 1; 128998224914431, 1; 312278175742409, 1
18^59+1 = [19, 1; 7907, 1
15^63-1 = [2, 1; 7, 2; 43, 1; 127, 1; 241, 1; 541, 1; 883, 1; 21061, 1; 123229, 1; 399043, 1; 1743463, 1; 1470374630929, 1; 2817034275427, 1
15^63+1 = [2, 4; 19, 1; 211, 1; 739, 1; 811, 1; 723031, 1; 10137331, 1; 10678711, 1; 48675439, 1; 191354311, 1
35^48+1 = [2, 1; 577, 1; 13921, 1; 188833, 1; 767008609, 1; 4394231174092284521569, 1
20^57-1 = [19, 2; 229, 1; 421, 1; 75368484119, 1; 192696104561, 1; 1374892397251, 1
20^57+1 = [3, 2; 7, 1; 127, 1; 6841, 1; 109850818001, 1; 222155207347, 1; 2272727294381, 1; 68465688966343, 1
19^58+1 = [2, 1; 181, 1; 929, 1; 4409, 1; 103114489, 1; 22716352849, 1; 7876159445929, 1
41^46+1 = [2, 1; 29, 2; 19318316874022005768653, 1
38^47-1 = [37, 1; 283, 1; 385662299007667579, 1
38^47+1 = [3, 1; 13, 1; 5641, 1; 13247559967, 1; 17828764795256160548561567779, 1
45^45-1 = [2, 2; 11, 1; 19, 1; 31, 1; 109, 1; 181, 1; 1471, 1; 2851, 1; 10009, 1; 135721, 1; 183451, 1; 283771, 1; 829639, 1; 2891101, 1; 134407081, 1; 1803639511, 1
45^45+1 = [2, 1; 7, 1; 23, 1; 41, 1; 61, 1; 283, 1; 7309, 1; 97841, 1; 1136089, 1; 44573401, 1; 427841641, 1; 1099730881, 1; 281780428261, 1
33^49-1 = [2, 5; 421, 1; 883, 1; 3163483, 1; 3576646417, 1
33^49+1 = [2, 1; 17, 1; 29, 1; 197, 1; 219409, 1; 20140079, 1; 2288452895246109846849799, 1
14^65-1 = [11, 1; 13, 2; 157, 1; 2081, 1; 3761, 1; 548055041, 1; 29914249171, 1
14^65+1 = [3, 1; 5, 2; 71, 1; 79, 1; 101, 1; 131, 1; 911, 1; 7307, 1; 100621, 1; 1812721, 1; 89590931, 1; 154160620391311, 1
24^54+1 = [13, 1; 37, 1; 73, 1; 109, 1; 349, 1; 577, 1; 875341, 1; 5273677, 1; 187162849, 1; 7973048859509888389, 1
31^50+1 = [2, 1; 13, 1; 37, 1; 181, 1; 1601, 1; 4707206941, 1
29^51-1 = [2, 2; 7, 1; 13, 1; 67, 1; 103, 1; 3911, 1; 1977917, 1; 48426439, 1; 1100628349, 1; 33505187587603, 1
29^51+1 = [2, 1; 3, 2; 5, 1; 271, 1; 1973, 1; 1288057, 1; 3877667, 1; 6212923, 1; 31618925959007, 1
13^67-1 = [2, 2; 3, 1; 586079017, 1; 1093561021297, 1; 1195860242597359, 1
13^67+1 = [2, 1; 7, 1; 269, 1; 4021, 1; 138959, 1; 28376556792667, 1
42^46+1 = [5, 1; 277, 1; 353, 1; 173735224109, 1; 267249548501187589, 1
39^47-1 = [2, 1; 19, 1; 156958009406747970486961183, 1
39^47+1 = [2, 3; 5, 1; 283, 1; 193547067732653, 1
23^55-1 = [2, 1; 11, 2; 292561, 1; 3468301, 1; 3937230404603, 1
23^55+1 = [2, 3; 3, 1; 31, 1; 41, 1; 211, 1; 20681, 1; 44771, 1; 62701, 1; 39700406579747, 1
26^53-1 = [5, 2; 4241, 1; 150097, 1; 358043142577, 1; 1971203353831, 1
26^53+1 = [3, 3; 107, 1; 2333, 1; 5156527199, 1; 54865399436668796181164201, 1
34^49-1 = [3, 1; 11, 1; 197, 1; 463, 1; 3437617, 1; 14582510251, 1; 234385605791, 1
34^49+1 = [5, 1; 7, 3; 29, 1; 71, 1; 104119, 1; 166700843, 1
17^61-1 = [2, 4; 15103230859721, 1
17^61+1 = [2, 1; 3, 2; 1831, 1; 536801, 1; 528720501902111, 1
43^46+1 = [2, 1; 5, 2; 37, 1
22^56+1 = [17, 1; 3227992561, 1; 127682309142529, 1; 6431392860517903090849, 1
28^52+1 = [614657, 1; 3398337641329450355189472420954977, 1
15^64+1 = [2, 1; 151553, 1; 70237697, 1; 17347644250739140028840698753, 1
37^48+1 = [2, 1; 97, 1; 5566657, 1; 1108161677126609953, 1
40^47-1 = [3, 1; 13, 1; 1289733970477, 1
40^47+1 = [41, 1; 7333, 1; 128969, 1; 83061617339, 1; 526353700325012837, 1
18^60+1 = [113, 1; 241, 1; 881, 1; 929, 1; 11019855601, 1; 495520919281, 1; 137841514501966721, 1
30^51-1 = [7, 2; 19, 1; 29, 1; 103, 1; 409, 1; 10570676926829627653, 1
30^51+1 = [13, 1; 31, 1; 67, 1; 613, 1; 7243, 1; 565727, 1; 165849348647, 1; 42840326829523, 1
21^57-1 = [2, 2; 5, 1; 463, 1; 304609, 1; 12061389013, 1; 54921106624003, 1
21^57+1 = [2, 1; 11, 1; 421, 1; 609673, 1; 5285953, 1; 67505443, 1; 987749814642143197, 1
19^59-1 = [2, 1; 3, 2
19^59+1 = [2, 2; 5, 1; 33179477, 1; 26886160879, 1
20^58+1 = [401, 1; 1063721, 1; 500140961, 1; 25104088611489177761, 1
44^46+1 = [13, 1; 149, 1; 66977, 1; 101638289, 1; 127237013, 1; 863831609, 1
14^66+1 = [37, 1; 197, 1; 1033, 1; 32341, 1; 88001, 1; 327889, 1; 2283733, 1; 240159217, 1; 3938797853, 1
35^49-1 = [2, 1; 17, 1; 43, 1; 225989, 1; 44007727, 1; 190753265393077226220781, 1
35^49+1 = [2, 2; 3, 2; 29, 1; 491, 1; 5209, 1; 11831, 1; 3200070539, 1; 9749772905251, 1; 5662939263847472419, 1
13^68+1 = [2, 1; 137, 1; 409, 1; 14281, 1; 63104137, 1
41^47-1 = [2, 3; 5, 1; 9958064719328486531, 1; 78094180566830018266230133, 1
41^47+1 = [2, 1; 3, 1; 7, 1; 659, 1; 1223, 1; 2021377, 1
38^48+1 = [97, 1; 11329, 1; 1495297, 1; 71918657, 1; 91752481, 1; 476743489, 1; 175779617473, 1
24^55-1 = [23, 1; 67, 1; 7349, 1; 346201, 1; 434501, 1; 134367047, 1; 340245936911, 1; 105562680440614871, 1
24^55+1 = [5, 3; 11, 2; 5791, 1; 28295741, 1; 65397751, 1; 60867245726761, 1
33^50+1 = [2, 1; 5, 3; 41, 1; 61, 1; 109, 1; 3701, 1; 4721, 1; 23801, 1; 81101, 1; 742226569901, 1; 12209956343835001, 1
29^52+1 = [2, 1; 353641, 1; 19589753, 1; 12453708073, 1; 1860604084769, 1
45^46+1 = [2, 1; 1013, 1; 76598585809, 1
31^51-1 = [2, 1; 3, 2; 5, 1; 331, 1; 1961163283, 1; 751670559138758105956097, 1
31^51+1 = [2, 5; 7, 2; 19, 1; 103, 1; 2796214962413636917873, 1; 6841661642646463343047, 1
23^56+1 = [2, 1; 17, 1; 113, 1; 449, 1; 3697, 1; 623009, 1; 9619978817, 1
17^62+1 = [2, 1; 5, 1; 29, 1; 2729, 1; 759322433, 1; 23321390258237, 1; 729426109307672111981, 1
42^47-1 = [41, 1; 283, 1; 169483, 1; 233753749, 1; 476181198178427051, 1
42^47+1 = [43, 1; 6299, 1
39^48+1 = [2, 1; 97, 1; 1409, 1; 5857, 1; 2240737, 1; 3745537, 1; 2713804961192257, 1
26^54+1 = [181, 1; 677, 1; 757, 1; 1621, 1; 2521, 1; 78020713, 1; 77768062633, 1; 89761824918036320617, 1
15^65-1 = [2, 1; 7, 1; 11, 1; 53, 1; 131, 1; 4931, 1; 157483, 1; 16655159, 1
15^65+1 = [2, 4; 31, 1; 79, 1; 1531, 1; 1294671691, 1; 1539711288259, 1; 118991428865318211233461, 1
46^46+1 = [29, 1; 73, 1; 1013, 1; 14629, 1; 31741, 1; 2221903165650473, 1; 617663426850071093, 1
22^57-1 = [3, 2; 7, 1; 13, 2; 2281, 1; 30097, 1; 45943, 1; 200983, 1; 341203, 1; 734186407417, 1; 97404596002423, 1
22^57+1 = [23, 1; 463, 1; 9007, 1; 9740503, 1; 23967703, 1; 37795766089771, 1; 58167002655376561, 1
18^61-1 = [17, 1; 367831, 1; 4110876980385153863, 1
18^61+1 = [19, 1; 703819, 1; 42043094784045697444762222723, 1
34^50+1 = [13, 1; 89, 1; 101, 1; 2801, 1; 663001, 1; 1784250435661, 1; 41595701549695208056901, 1
21^58+1 = [2, 1; 13, 1; 17, 1; 349, 1; 18097, 1; 1792484183066669, 1
28^53-1 = [3, 3; 220187971, 1
28^53+1 = [29, 1; 107, 1; 2336285687, 1; 309617974423, 1
19^60+1 = [2, 1; 17, 1; 41, 1; 3833, 1; 4297, 1; 3952393, 1; 478382041, 1; 14706033761, 1
20^59-1 = [19, 1; 709, 1; 32031477011, 1; 50552666868943321, 1; 4443043113983919668779, 1
20^59+1 = [3, 1; 7, 1; 2505995335981, 1; 60435208609469, 1
43^47-1 = [2, 1; 3, 1; 7, 1; 108788243190817386661, 1
43^47+1 = [2, 2; 11, 1; 283, 1; 659, 1; 13913, 1; 24921448261, 1; 14108231161651413422411, 1
14^67-1 = [13, 1; 269, 1; 12329, 1; 169913, 1; 2516066164220253191649971614939, 1
14^67+1 = [3, 1; 5, 1; 86029, 1; 16731682871, 1; 742346622710948405402237, 1
30^52+1 = [241, 1; 313, 1; 3361, 1; 10708105609969, 1; 2017218763920257, 1
37^49-1 = [2, 2; 3, 2; 71, 1; 197, 1; 491, 1; 119267, 1; 37140797, 1; 264423311286840201546264901, 1
37^49+1 = [2, 1; 19, 1; 2498207293, 1; 351185187025039935877, 1; 351405021365451201191, 1
13^69-1 = [2, 2; 3, 2; 61, 1; 139, 1; 1381, 1; 10903, 1; 282244620282733, 1; 2519545342349331183143, 1
13^69+1 = [2, 1; 7, 1; 47, 1; 157, 1; 277, 1; 1151, 1; 2347, 1; 7039, 1; 84801400975699, 1
40^48+1 = [97, 1; 8641, 1; 1044193, 1; 4970451679203795856961, 1
35^50+1 = [2, 1; 101, 1; 181, 1; 613, 1; 12431152621, 1; 407991287029853801, 1
44^47-1 = [43, 1; 659, 1; 4231, 1; 152939, 1; 224409680922367, 1; 384826871364277, 1
44^47+1 = [3, 2; 5, 1; 8073473, 1; 368082287, 1; 111180004905719552711742659081, 1
24^56+1 = [17, 1; 113, 1; 2801, 1; 2311681, 1; 2603441, 1; 12175852634824817, 1
38^49-1 = [37, 1; 883, 1; 1471, 1; 1295953, 1; 3092313043, 1; 6089952760761349033, 1
38^49+1 = [3, 1; 13, 1; 29, 1; 239, 1; 423277, 1; 519107, 1; 156268094118473, 1; 251921653503938153, 1
41^48+1 = [2, 1; 97, 1; 334177, 1; 2333857, 1; 18096796400991457, 1; 2969334894856405949761, 1
33^51-1 = [2, 5; 103, 1; 1123, 1; 82723, 1; 113357, 1; 191251, 1; 241333, 1; 1137388061, 1
33^51+1 = [2, 1; 7, 1; 17, 2; 151, 1; 5407, 1; 1435438759, 1; 132345083573, 1; 853299177421, 1
29^53-1 = [2, 2; 7, 1; 107, 1; 10601, 1
29^53+1 = [2, 1; 3, 1; 5, 1; 187091, 1; 102968016651034826283138186847, 1
17^63-1 = [2, 4; 19, 1; 43, 1; 127, 1; 307, 1; 13567, 1; 1270657, 1; 25646167, 1; 940143709, 1; 41643373496311819, 1
17^63+1 = [2, 1; 3, 4; 7, 2; 13, 1; 1423, 1; 5653, 1; 12404449, 1; 22796593, 1; 59044357, 1; 428802078097, 1; 88109799136087, 1
31^52+1 = [2, 1; 409, 1; 1129, 1; 305688893141113, 1; 5603212901768856193, 1
23^57-1 = [2, 1; 7, 1; 11, 1; 79, 1; 2129, 1; 63877469, 1; 2350382803, 1; 24939218613613, 1; 1420450672756039, 1
23^57+1 = [2, 3; 3, 2; 13, 2; 493811, 1; 3195383, 1; 1970307281599, 1; 58531113508957, 1
15^66+1 = [2, 1; 13, 1; 113, 1; 397, 1; 617, 1; 3877, 1; 63493, 1; 363567733, 1; 18510347197, 1; 536554814380116068153, 1
45^47-1 = [2, 2; 11, 1; 1129, 1; 154724189, 1; 51837304274143573658745029, 1
45^47+1 = [2, 1; 23, 1; 1055439443203, 1; 5007871893259011010762923469, 1
26^55-1 = [5, 3; 11, 2; 23, 1; 8641, 1; 65539, 1; 3279541, 1; 97395563, 1; 208341431, 1; 470196238294201, 1
26^55+1 = [3, 3; 431, 1; 1021, 1; 192458971, 1; 135938684703251, 1
18^62+1 = [5, 2; 13, 1; 373, 1; 1158037, 1; 89891941, 1; 844025609171791028413, 1
22^58+1 = [5, 1; 97, 1; 929, 1; 5905440414034349, 1
42^48+1 = [97, 1; 193, 1; 205633, 1; 385713217, 1; 97921741921, 1; 5007945605667365550817, 1
14^68+1 = [41, 1; 409, 1; 937, 1; 1198859041, 1
39^49-1 = [2, 1; 19, 1; 2857, 1; 398273, 1; 1264033, 1; 125273303, 1; 372358437809, 1; 3105873038176091, 1
39^49+1 = [2, 3; 5, 1; 43, 1; 71, 1; 197, 1; 1123739, 1; 6771507792824739072112812646693, 1
13^70+1 = [2, 1; 5, 2; 17, 1; 421, 1; 601, 1; 641, 1; 23161037562937, 1
19^61-1 = [2, 1; 3, 2
19^61+1 = [2, 2; 5, 1; 733, 1; 8053, 1; 84510011, 1; 1292509969, 1; 142920649702891953961, 1
21^59-1 = [2, 2; 5, 1; 896447, 1; 334217419, 1; 47540111129611360301, 1
21^59+1 = [2, 1; 11, 1; 3085597813, 1
20^60+1 = [241, 1; 31177, 1; 148721, 1; 160001, 1; 821113, 1; 22921681, 1; 4817246650081, 1; 4406613081041681, 1
34^51-1 = [3, 2; 11, 1; 103, 1; 137, 1; 397, 1; 919, 1; 1327, 1; 232846577043840572161, 1
34^51+1 = [5, 1; 7, 1; 307, 1; 443, 1; 1123, 1; 1531, 1; 7753, 1; 28051, 1; 112643, 1; 681259, 1; 4708729, 1
28^54+1 = [5, 1; 13, 1; 157, 1; 24481, 1; 47221, 1; 50221, 1; 314497, 1; 188878213, 1; 235922815189, 1; 428485444021, 1
46^47-1 = [3, 2; 5, 1; 941, 1; 16431429538240371836933, 1
46^47+1 = [47, 2; 659, 1
30^53-1 = [29, 1; 107, 1; 28027943525891113319, 1; 92062209914431198469, 1
30^53+1 = [31, 1; 18348714939299, 1; 408748358195077, 1
43^48+1 = [2, 1; 769, 1; 19681, 1; 20929, 1; 149377, 1; 878593, 1; 966913, 1; 103776599233, 1; 4513274958253588609, 1
37^50+1 = [2, 1; 5, 3; 61, 1; 137, 1; 81701, 1; 11507920001, 1; 20537546119484501, 1; 5153406763721063801, 1
40^49-1 = [3, 1; 13, 1; 197, 1; 4201025641, 1; 36470521116165877118530363, 1
40^49+1 = [41, 1; 211, 1; 18938851, 1
47^47-1 = [2, 1; 23, 1; 1693, 1; 255742492896763511474638530188876017, 1
47^47+1 = [2, 4; 3, 1; 659, 1; 15511, 1; 65519, 1; 21179047, 1; 10519189757, 1; 60963223421, 1; 2506611914519, 1
24^57-1 = [23, 1; 457, 1; 601, 1; 4219, 1; 112950414769, 1; 7282588256957615350925401, 1
24^57+1 = [5, 2; 7, 1; 79, 1; 3810589537, 1; 121954170337, 1; 6699981196401006122851369, 1
35^51-1 = [2, 1; 13, 1; 17, 2; 97, 1; 1780003, 1; 1714059307, 1; 172507579403449211, 1
35^51+1 = [2, 2; 3, 3; 103, 1; 307, 1; 397, 1; 51817, 1; 124615474273, 1; 309915724674603539, 1
17^64+1 = [2, 1; 769, 1; 138497, 1
15^67-1 = [2, 1; 7, 1; 4954919, 1; 2628501058611905652954840361379, 1
15^67+1 = [2, 4; 93348019, 1; 21737518025925979, 1
44^48+1 = [197352587024076973231046657, 1
33^52+1 = [2, 1; 97, 1; 6113, 1; 394577, 1
29^54+1 = [2, 1; 37, 1; 61, 1; 313, 1; 421, 1; 757, 1; 4978801, 1; 467390730000853, 1; 42150482650323109, 1
23^58+1 = [2, 1; 5, 1; 53, 1; 929, 1; 15313, 1
38^50+1 = [5, 3; 17, 2; 61, 1; 101, 1; 38201, 1; 372901, 1; 720301, 1; 1712401, 1
41^49-1 = [2, 3; 5, 1; 43, 1; 6763, 1; 113229229, 1; 262710757, 1; 125400466409, 1
41^49+1 = [2, 1; 3, 1; 7, 3; 71, 1; 197, 1; 1583093, 1; 9329993, 1; 57338233, 1; 1321395937, 1; 12151537468866066797, 1
31^53-1 = [2, 1; 3, 1; 5, 1; 218149, 1; 2210276655188599, 1; 1593405992841712852324481273, 1
31^53+1 = [2, 5; 107, 1; 1061, 1; 83423, 1; 185183, 1; 19503537629, 1; 88387933035190440551, 1
18^63-1 = [7, 4; 17, 1; 127, 1; 449, 1; 631, 1; 991, 1; 2143, 1; 34327, 1; 80207, 1; 1292257, 1; 156107192084257, 1
18^63+1 = [19, 1; 43, 1; 73, 1; 307, 1; 46747, 1; 465841, 1; 32222107, 1; 337268233, 1; 607371619, 1
14^69-1 = [13, 1; 47, 1; 211, 1; 461, 1; 2347, 1; 10627, 1; 2249861, 1; 14525237, 1; 812293117, 1; 2609588427937, 1
14^69+1 = [3, 2; 5, 1; 61, 1; 139, 1; 691, 1; 967, 1; 12431317, 1; 19922509, 1; 5715684596759, 1
13^71-1 = [2, 2; 3, 1; 6959, 1; 12923, 1; 201499, 1
13^71+1 = [2, 1; 7, 1; 532615479720542238328159944384931, 1
22^59-1 = [3, 1; 7, 1; 2288129166742313, 1
22^59+1 = [23, 1; 1005612521, 1; 445117398832960434677, 1
26^56+1 = [3617, 1; 30689, 1; 297809, 1; 5831057, 1; 57734881, 1; 378275286403075217297, 1
19^62+1 = [2, 1; 181, 1; 373, 1; 774629, 1; 743762742808750682665930129, 1
21^60+1 = [2, 1; 73, 1; 601, 1; 97241, 1; 3441241, 1; 40086001, 1; 518118697, 1; 415710882920521, 1
45^48+1 = [2, 1; 97, 1; 449, 1; 35521, 1; 191137, 1; 1383169, 1; 12278127457, 1
20^61-1 = [19, 1; 1831, 1; 1575631, 1; 74324733207911, 1
20^61+1 = [3, 1; 7, 1; 12287385389923456825324271923, 1
42^49-1 = [41, 1; 197, 1; 491, 1; 3851, 1; 145139, 1; 1460117, 1
42^49+1 = [29, 1; 43, 1; 337, 1; 5783, 1; 548591, 1; 3262238798491, 1
39^50+1 = [2, 1; 41, 1; 101, 1; 761, 1; 1901, 1; 24170501, 1; 1291594501, 1; 72218350982497903814401, 1
28^55-1 = [3, 3; 637421, 1; 6077039, 1; 50545507, 1; 16071033331, 1; 829366011211, 1; 94275090945167441, 1
28^55+1 = [11, 2; 23, 2; 29, 1; 53951, 1; 346438463911, 1; 540610746853, 1
34^52+1 = [521, 1; 7177, 1; 1336337, 1; 2536873, 1; 133669433, 1; 3346237441, 1; 1296816525740341450729, 1
30^54+1 = [17, 1; 53, 1; 109, 1; 809101, 1; 11004811314110641, 1; 531440999271000001, 1
46^48+1 = [97, 1; 577, 1; 1249, 1; 8513, 1; 20641, 1; 624737, 1; 3429697, 1; 779065031672321, 1
15^68+1 = [2, 1; 17, 2; 1489, 1; 9929, 1
37^51-1 = [2, 2; 3, 3; 7, 1; 67, 1; 613, 1; 109172471, 1; 161934782169241, 1; 189475557532747, 1
37^51+1 = [2, 1; 19, 1; 31, 1; 43, 1; 103, 1; 115873, 1; 560276923, 1; 159012729398779, 1; 15142988434621452581641, 1
17^65-1 = [2, 4; 88741, 1; 212057, 1; 9882731, 1; 2919196853, 1; 42774218980741, 1
17^65+1 = [2, 1; 3, 2; 11, 1; 53, 1; 71, 1; 79, 1; 101, 1; 131, 1; 53171, 1; 65651, 1; 2001793, 1; 346638477380024845861, 1
43^49-1 = [2, 1; 3, 1; 7, 3; 491, 1; 5839, 1; 158341, 1
43^49+1 = [2, 2; 11, 1; 197, 1; 18229, 1; 6177695707, 1; 12324475400273, 1; 111426688573308893, 1
24^58+1 = [577, 1; 129457, 1
40^50+1 = [101, 1; 241, 1; 281, 1; 1601, 1; 5501, 1; 17581, 1; 174101, 1; 2198701, 1; 13437901, 1; 145152101, 1; 253759201, 1
13^72+1 = [2, 1; 1009, 1; 3889, 1; 680401, 1; 407865361, 1; 29975087953, 1; 659481276875569, 1; 6654909974864689, 1
14^70+1 = [29, 2; 113, 1; 197, 1; 281, 1; 1061, 1; 3361, 1; 22961, 1; 176597, 1; 1383881, 1; 169104974081, 1; 179266059891241, 1
47^48+1 = [2, 1; 5441, 1; 528002017, 1; 98678246569313, 1; 1148340356764147681, 1
35^52+1 = [2, 1; 3329, 1; 750313, 1; 45467449, 1; 112487060401, 1
18^64+1 = [257, 1; 769, 1
23^59-1 = [2, 1; 11, 1; 5995817, 1; 451573729, 1; 15648899754659, 1; 3794908745134333508761, 1
23^59+1 = [2, 3; 3, 1; 11801, 1; 3193789, 1; 121570269892408921, 1
29^55-1 = [2, 2; 7, 1; 23, 1; 338141, 1; 732541, 1; 1193512007711, 1; 18944890940537, 1; 13323049382040421, 1
29^55+1 = [2, 1; 3, 1; 5, 2; 11, 2; 31, 1; 401, 1; 5618383, 1; 72384467, 1; 78400741, 1; 41281260791, 1
33^53-1 = [2, 5; 107, 1; 6422603005129, 1; 4614550029643428870259710306803, 1
33^53+1 = [2, 1; 17, 1; 618577813640557, 1
44^49-1 = [43, 1; 239, 1; 1163, 1; 1373, 1; 26713, 1; 545959, 1
44^49+1 = [3, 2; 5, 1; 20287, 1; 643273, 1; 2192261, 1; 7095062437, 1; 12724778641, 1; 14266041791, 1; 318781334420123, 1
31^54+1 = [2, 1; 13, 1; 37, 1; 922561, 1; 1536553, 1; 512616735577, 1; 277477787226853, 1; 91556360840213317, 1
22^60+1 = [41, 1; 73, 1; 3209, 1; 21001, 1; 191353, 1; 286777, 1; 6298801, 1; 305490121, 1; 240425214401, 1
19^63-1 = [2, 1; 3, 4; 127, 1; 523, 1; 701, 1; 29989, 1; 70841, 1; 30640261, 1; 68443621, 1; 21095068697641, 1
19^63+1 = [2, 2; 5, 1; 7, 4; 43, 2; 197, 1; 199, 1; 226871, 1; 236377, 1; 343393, 1; 524119, 1; 204396571, 1; 68338204247969587, 1
38^51-1 = [37, 1; 103, 1; 137, 1; 1483, 1; 151471, 1; 4269211, 1; 33193361176106273, 1
38^51+1 = [3, 2; 7, 1; 13, 1; 67, 1; 307, 1; 289001, 1; 45909793, 1; 4521822181, 1
41^50+1 = [2, 1; 29, 2; 101, 1; 761, 1; 40312301, 1; 103826101, 1; 1069778710978086022057601, 1
26^57-1 = [5, 2; 19, 2; 37, 1; 1597, 1; 33403, 1; 551192154259, 1; 54509933224633, 1; 916631343715906315531, 1
26^57+1 = [3, 4; 7, 1; 31, 1; 229, 1; 6753589, 1; 50288585161, 1; 123963652789966341658519, 1
21^61-1 = [2, 2; 5, 1; 15373, 1; 12519763, 1; 1128331159687, 1; 1814065850324073713, 1
21^61+1 = [2, 1; 11, 1; 367, 1; 75641, 1; 15569711981, 1; 132538677158969693, 1; 37376752870606823789, 1
20^62+1 = [373, 1; 401, 1; 111160667194373, 1
48^48+1 = [769, 1; 45121, 1; 170497, 1; 2492087396737, 1; 4657394825125242693121, 1
45^49-1 = [2, 2; 11, 1; 29, 1; 71, 1; 1199521, 1; 4124569, 1; 916663899843735821, 1
45^49+1 = [2, 1; 23, 1; 43, 1; 15146783, 1; 188912767, 1; 14515265795378503, 1
28^56+1 = [17, 1; 7841, 1; 22223646961, 1
39^51-1 = [2, 1; 7, 1; 19, 1; 223, 1; 312971, 1; 93931363225910189411, 1
39^51+1 = [2, 3; 5, 1; 103, 1; 919, 1; 1327, 1; 1483, 1; 2487713, 1; 7585029579997, 1; 108993557443570343, 1
15^69-1 = [2, 1; 7, 1; 241, 1; 829, 1; 967, 1; 31741, 1; 434956681, 1; 80732172121, 1; 3046462151831565769, 1
15^69+1 = [2, 4; 47, 1; 139, 1; 211, 1; 1381, 1; 6257, 1; 81421, 1; 825287, 1; 3549551867, 1
42^50+1 = [5, 3; 101, 1; 353, 1; 2521, 1; 9181, 1; 83621, 1; 1087301, 1; 60031801, 1; 408815101, 1; 58728331301, 1
34^53-1 = [3, 1; 11, 1; 107, 1; 1081307, 1; 2594987, 1; 12864479, 1
34^53+1 = [5, 1; 7, 1; 687636463277, 1; 1658423715104692910299, 1; 1900676816200539211871, 1
17^66+1 = [2, 1; 5, 1; 29, 1; 89, 1; 397, 1; 19801, 1; 25741, 1; 83233, 1; 85009, 1; 256152733, 1; 6901823633, 1
30^55-1 = [29, 1; 1321, 1; 837931, 1; 81370145080291, 1; 610851724137931, 1; 9119031913911026141, 1
30^55+1 = [11, 2; 23, 1; 31, 1; 71261, 1; 88793, 1; 279811489, 1; 492541370954042703727521011, 1
13^73-1 = [2, 2; 3, 1; 145009586102490829218552548223336637, 1
13^73+1 = [2, 1; 7, 1; 45553, 1; 64803179963, 1
14^71-1 = [13, 1; 4261, 1; 954519632047180992533553119, 1
14^71+1 = [3, 1; 5, 1; 569, 1; 3620291, 1; 56165234981886479394192094297061, 1
24^59-1 = [23, 1; 3156383, 1; 40322995067713, 1; 20058520782729629621, 1
24^59+1 = [5, 2; 827, 1; 103947039333204799, 1; 32161793704106598258806381, 1
46^49-1 = [3, 2; 5, 1; 491, 1; 883, 1; 1471, 1; 3060247, 1; 9684836827, 1
46^49+1 = [47, 1; 3137, 1; 540961, 1; 9272716111, 1; 166685262353, 1; 1712624274562699, 1
37^52+1 = [2, 1; 89, 1; 10529, 1; 219509124812279641, 1; 257572786301234791762248953, 1
18^65-1 = [17, 1; 41, 1; 79, 1; 521, 1; 911, 1; 2711, 1; 29759719289, 1; 260674349667764744544365521, 1
18^65+1 = [11, 1; 19, 1; 131, 1; 2081, 1; 3121, 1; 9041, 1; 2570316451, 1; 4020180841, 1; 3242950762090314211, 1
43^50+1 = [2, 1; 5, 4; 37, 1; 41, 1; 4481, 1; 243701, 1; 12716981, 1; 187654333501, 1
23^60+1 = [2, 1; 937, 1; 1801, 1; 5081, 1; 139921, 1; 5670961, 1; 83575993, 1; 76384053703681, 1; 1206964869343609001, 1
40^51-1 = [3, 2; 13, 1; 239, 1; 547, 1; 2347, 1; 331205867, 1; 556492509861557, 1; 25161597834306874249, 1
40^51+1 = [7, 1; 41, 1; 103, 1; 223, 1; 647, 1; 4007921, 1; 16158928623546703, 1
35^53-1 = [2, 1; 17, 1; 107, 1; 1061, 1
35^53+1 = [2, 2; 3, 2; 836420846435311309, 1
19^64+1 = [2, 1; 36097, 1; 87553, 1; 315989504252280687606137174469121, 1
22^61-1 = [3, 1; 7, 1; 733, 1; 188369, 1; 13531997, 1; 1078645984686904783, 1
22^61+1 = [23, 1; 650493602920343105522571195991702169, 1
29^56+1 = [2, 1; 17, 1; 113, 1; 26209, 1; 561377, 1; 9177760265723729, 1; 30956385805538033, 1
47^49-1 = [2, 1; 23, 1; 43, 1; 256128979, 1; 32620302149, 1
47^49+1 = [2, 4; 3, 1; 197, 1; 5881, 1; 1794703, 1; 31601224255465429885537422388541, 1
20^63-1 = [19, 1; 29, 1; 71, 1; 421, 1; 6679, 1; 32719, 1; 460951, 1; 64008001, 1; 8442733531, 1
20^63+1 = [3, 3; 7, 2; 43, 1; 127, 1; 307, 1; 827, 1; 10529, 1; 69481, 1; 2750161, 1; 36363727, 1
21^62+1 = [2, 1; 13, 1; 17, 1; 66713, 1; 92753, 1; 13163658325422541897, 1
33^54+1 = [2, 1; 5, 1; 13, 1; 109, 1; 91141, 1; 123553, 1; 49552308901, 1; 878338391619313, 1; 1667889513661516993, 1
31^55-1 = [2, 1; 3, 1; 5, 2; 11, 2; 23, 1; 397, 1; 617, 1; 17351, 1; 150332843, 1; 167767051, 1
31^55+1 = [2, 5; 41, 1; 661, 1; 2531, 1; 11551, 1; 21821, 1; 757241, 1; 1048563011, 1
26^58+1 = [233, 1; 677, 1; 79732359887603230302193, 1
38^52+1 = [41, 1; 50857, 1; 5946019561, 1
44^50+1 = [13, 1; 101, 1; 149, 1; 541, 1; 5126701, 1; 256967681, 1; 94054066706799371868853565701, 1
41^51-1 = [2, 3; 5, 1; 103, 1; 1723, 1; 791419, 1; 201815909, 1; 323824851129646973, 1
41^51+1 = [2, 1; 3, 2; 7, 1; 547, 1; 1021, 1; 62240958750018457814374721, 1
15^70+1 = [2, 1; 29, 1; 113, 1; 19421, 1; 131381, 1; 531581, 1; 363860910841, 1; 4454215139669, 1
48^49-1 = [47, 1; 71, 1; 175926983, 1; 69178543169487767, 1; 96313641291003767, 1
48^49+1 = [7, 4; 1711569511, 1; 121472224903, 1; 11495423671999, 1; 279307608307476013861, 1
13^74+1 = [2, 1; 5, 1; 17, 1; 149, 1; 1738568407946597, 1
17^67-1 = [2, 4; 436171, 1
17^67+1 = [2, 1; 3, 2; 7103, 1; 369966985497341977627, 1
28^57-1 = [3, 4; 271, 1; 457, 1; 90403, 1; 21084187, 1; 62830837877749, 1; 5504044949138999959, 1
28^57+1 = [29, 1; 757, 1; 7508041, 1; 108044981035496842464510517, 1
14^72+1 = [17, 1; 5393, 1; 16097, 1; 19489, 1; 722833, 1; 154604113, 1; 288392833, 1
45^50+1 = [2, 1; 601, 1; 1013, 1; 683401, 1; 2076001, 1; 16806825723601, 1; 182921405634402336001, 1
34^54+1 = [13, 1; 89, 1; 1069, 1; 1249, 1; 54829, 1; 1678429, 1; 43524789475429, 1; 888695745733365949, 1
30^56+1 = [337, 1; 401, 1; 4855073, 1; 28004369, 1; 824509729, 1; 87235391377, 1; 290221578517697, 1
39^52+1 = [2, 1; 521, 1; 398113, 1; 1156721, 1; 11825321, 1; 80082913, 1; 1211020240017749481737, 1
42^51-1 = [13, 1; 41, 1; 139, 1; 1158007, 1; 82935963690420160273, 1
42^51+1 = [43, 1; 103, 1; 1723, 1; 3877, 1; 89188964023736497, 1; 229317107671612604641, 1
24^60+1 = [41, 1; 97, 1; 331777, 1; 119179481, 1; 736452721, 1; 1134793633, 1; 1147229924161, 1; 2479666140481, 1
18^66+1 = [5, 2; 13, 1; 89, 1; 229, 1; 457, 1; 1321, 1; 1392733, 1; 1527087937, 1; 55547468813, 1; 2570735949673, 1; 8941138915237, 1
23^61-1 = [2, 1; 11, 1; 5266228211, 1; 4217468380980037880092527701441161, 1
23^61+1 = [2, 3; 3, 1; 36479, 1
37^53-1 = [2, 2; 3, 2; 107, 1; 743, 1; 1061, 1; 340690573, 1; 65705244907, 1
37^53+1 = [2, 1; 19, 1; 24624967, 1; 2478616339, 1; 3769340299477, 1; 19140189134660171629621, 1
19^65-1 = [2, 1; 3, 2; 151, 1; 599, 1; 911, 1; 29251, 1; 96851, 1; 38324521, 1; 52356721, 1; 133338869, 1; 153079681, 1
19^65+1 = [2, 2; 5, 2; 11, 1; 131, 1; 313, 1; 2251, 1; 176021, 1; 291331, 1; 77685006382386461342123321, 1
46^50+1 = [29, 1; 41, 1; 73, 1; 101, 1; 541, 1; 5101, 1; 177101, 1; 7544475331153046399106018968101, 1
22^62+1 = [5, 1; 97, 1; 4093, 1; 23298361, 1; 45727606853, 1; 13301795714853532637, 1
20^64+1 = [4213987444481, 1; 19781545588481, 1; 82832842974154279534081, 1
21^63-1 = [2, 2; 5, 1; 43, 1; 127, 1; 463, 1; 631, 1; 3319, 1; 4789, 1; 6427, 1; 51787, 1; 85775383, 1; 227633407, 1; 22125429901, 1; 27186384126763, 1
21^63+1 = [2, 1; 11, 1; 19, 1; 37, 1; 199, 1; 337, 1; 421, 1; 613, 1; 516349, 1; 734329, 1; 81867661, 1; 22864311556633, 1; 4527391635851869, 1
43^51-1 = [2, 1; 3, 2; 7, 1; 613, 1; 631, 1; 647, 1; 1022492881, 1; 56770350869, 1; 3807926835707, 1
43^51+1 = [2, 2; 11, 1; 13, 1; 103, 2; 139, 1; 28867, 1; 4917999089, 1; 1098988543267429, 1; 27147048848953409, 1
40^52+1 = [313, 1; 769, 1; 3329, 1; 1532427957386458474991124529, 1
29^57-1 = [2, 2; 7, 1; 13, 1; 67, 1; 571, 1; 11971, 1; 73303, 1; 1386659, 1; 274773085966123, 1; 157193380600163813309, 1
29^57+1 = [2, 1; 3, 2; 5, 1; 271, 1; 457, 1; 16759, 1; 12139270932215509058971, 1
35^54+1 = [2, 1; 37, 1; 73, 1; 277, 1; 613, 1; 5413, 1; 28297, 1; 1251099780162301, 1
26^59-1 = [5, 2; 3541, 1; 334945708538658924935948356996883525107, 1
26^59+1 = [3, 3; 254250862891621, 1
15^71-1 = [2, 1; 7, 1; 91733, 1; 5957753, 1; 272301574062887284439621057578687, 1
15^71+1 = [2, 4; 5852594044699, 1; 922195312138651, 1; 6713182133980505226300443, 1
31^56+1 = [2, 1; 17, 1; 2129, 1; 27329, 1; 25085030513, 1; 3117962927633, 1
33^55-1 = [2, 5; 31, 1; 331, 1; 2113, 1; 8581, 1; 39451, 1; 204970261, 1; 47284185301, 1; 180115639771, 1; 747487377451, 1
33^55+1 = [2, 1; 17, 1; 23, 1; 1871, 1; 1151041, 1; 34544013769, 1
13^75-1 = [2, 2; 3, 2; 61, 1; 701, 1; 1951, 1; 4651, 1; 9851, 1; 30941, 1; 161971, 1; 2752135920929651, 1
13^75+1 = [2, 1; 7, 1; 11, 1; 31, 1; 101, 1; 151, 1; 157, 1; 2411, 1; 11551, 1; 57751, 1; 2113801, 1; 28325071, 1; 966623849742301, 1; 3258254426373251, 1
47^50+1 = [2, 1; 5, 3; 13, 1; 17, 1; 521, 1; 27901, 1; 260201, 1; 9136473061, 1; 594553745104018868744801, 1
14^73-1 = [13, 1; 439, 1; 7708818770493814043599025468833, 1
14^73+1 = [3, 1; 5, 1; 293, 1; 124195272375239203, 1
17^68+1 = [2, 1; 41761, 1; 104466451393, 1
38^53-1 = [37, 1; 743, 1; 1114177494385601, 1; 74299888772887067959, 1
38^53+1 = [3, 1; 13, 1; 107, 1; 2969, 1; 5239571773129, 1
44^51-1 = [7, 1; 43, 1; 283, 1; 14519, 1; 113744216251, 1; 13908821686834391538539, 1
44^51+1 = [3, 3; 5, 1; 103, 1; 631, 1; 19891, 1; 9014673097, 1; 21405875942779901, 1
41^52+1 = [2, 1; 137, 1; 10313, 1; 10867897, 1; 67794169, 1
28^58+1 = [5, 1; 157, 1; 233, 1; 349, 1; 708359326721, 1
48^50+1 = [5, 3; 101, 1; 461, 1; 1326539778001, 1; 5633411028941, 1; 8095020975930143401, 1
18^67-1 = [17, 1; 864167, 1; 14184594510552113, 1; 562081533912939823, 1
18^67+1 = [19, 1; 100254379, 1; 14597889070451, 1; 17412147374909347, 1
24^61-1 = [23, 1; 15739, 1; 1416951311, 1; 1858425216920537117, 1; 3111460356271636883680109, 1
24^61+1 = [5, 2; 367, 1; 8034799, 1; 93359647, 1; 977208959123, 1; 61357956800593, 1; 1460314542488141, 1
30^57-1 = [7, 2; 19, 2; 29, 1; 191, 1; 33189733, 1; 316011085610449051, 1; 2098323645062285611121141, 1
30^57+1 = [13, 1; 31, 1; 67, 1; 2281, 1; 226758997, 1; 60563288311, 1; 1653398801508051043, 1
34^55-1 = [3, 1; 11, 2; 61, 1; 22571, 1; 45343, 1; 49831, 1; 4264333987, 1
34^55+1 = [5, 2; 7, 1; 23, 1; 259631, 1; 56233934021, 1; 87191110109357, 1; 75163328903964097539601, 1
45^51-1 = [2, 2; 11, 1; 19, 1; 109, 1; 1531, 1; 188879518520424412857091, 1; 33009788025075117650794669, 1
45^51+1 = [2, 1; 7, 1; 23, 1; 103, 1; 283, 1; 409, 1; 68443, 1; 102103, 1; 29335436267, 1; 2769417107629327, 1; 9428928689731043, 1
39^53-1 = [2, 1; 19, 1; 107, 1; 3923, 1; 2368685761590563, 1
39^53+1 = [2, 3; 5, 1; 5407, 1; 170010978689372035136190196567, 1
19^66+1 = [2, 1; 13, 2; 181, 1; 769, 1; 774797, 1; 205228610269, 1; 48381877771677135533, 1
42^52+1 = [17, 1; 313, 1; 183041, 1
23^62+1 = [2, 1; 5, 1; 53, 1; 373, 1; 21711433659565142917, 1
20^65-1 = [11, 1; 19, 1; 61, 1; 131, 1; 251, 1; 521, 1; 3121, 1; 3511, 1; 4421, 1; 90481, 1; 142559, 1; 9690539, 1; 4470064171, 1; 144142570154831, 1
20^65+1 = [3, 1; 7, 1; 2081, 1; 2549, 1; 152381, 1; 735408649, 1; 34458786390125761, 1
22^63-1 = [3, 3; 7, 2; 13, 2; 127, 1; 65899, 1; 297613, 1; 16968421, 1; 274392421115023, 1; 12271836836138419, 1
22^63+1 = [19, 1; 23, 1; 29, 1; 43, 1; 463, 1; 3571, 1; 86969, 1; 404671, 1; 5966803, 1; 9299179, 1; 22277258819047, 1
21^64+1 = [2, 1; 257, 1; 641, 1; 1409, 1; 527489, 1; 70660081537, 1
13^76+1 = [2, 1; 761, 1; 2281, 1; 14281, 1; 692513, 1; 62300665486585624081, 1
15^72+1 = [2, 1; 3169, 1; 7121, 1; 179953, 1; 1659649, 1; 1248882721, 1; 1076233596845085335953, 1
37^54+1 = [2, 1; 5, 1; 13, 1; 109, 1; 137, 1; 2917, 1; 144061, 1; 6582952003274308873, 1
46^51-1 = [3, 3; 5, 1; 7, 1; 103, 1; 1361, 1; 8059, 1; 8660100334911387121, 1; 301864818112420877836267, 1
46^51+1 = [19, 1; 47, 1; 109, 1; 409, 1; 3673, 1; 107093805778192889244007, 1
14^74+1 = [149, 1; 197, 1; 13270292968062854021, 1; 20869260239752113310657, 1
29^58+1 = [2, 1; 421, 1
26^60+1 = [17, 1; 41, 1; 1721, 1; 2081, 1; 26881, 1; 208826607601, 1; 296985885709361, 1; 7528533299625721, 1
17^69-1 = [2, 4; 47, 1; 307, 1; 25225573, 1; 9559382330644273, 1; 26552618219228090162977481, 1
17^69+1 = [2, 1; 3, 3; 7, 1; 13, 1; 139, 1; 1191693343, 1; 144905634142323992263, 1; 60844755602264877238459, 1
40^53-1 = [3, 1; 13, 1; 107, 1; 3710337187, 1; 1740695540599129, 1; 10682573878867427387, 1
40^53+1 = [41, 1
35^55-1 = [2, 1; 17, 1; 23, 1; 31, 1; 49831, 1; 55903, 1; 72271, 1; 2208546869, 1; 2260908423193372856201, 1
35^55+1 = [2, 2; 3, 2; 11, 2; 991, 1; 4951, 1; 132631, 1; 2681921038140191, 1; 1777716539623484791, 1
43^52+1 = [2, 1; 17, 1; 193, 1; 521, 1; 50440205609, 1; 359967267341875337, 1
50^50+1 = [41, 1; 61, 1; 101, 1; 62801, 1; 5122541, 1; 7622561, 1; 10946101, 1; 8903411298923101, 1; 10604434965481801, 1
31^57-1 = [2, 1; 3, 2; 5, 1; 331, 1; 571, 1; 7639, 1; 14251, 1; 36068660903683, 1; 88770666332610762169, 1
31^57+1 = [2, 5; 7, 2; 19, 2; 191, 1; 4903, 1; 1553023, 1; 98595072158281, 1; 3545592640701962728192781, 1
33^56+1 = [2, 1; 113, 1; 258721, 1; 384497, 1; 14937537217, 1; 703204309121, 1
47^51-1 = [2, 1; 23, 1; 37, 1; 61, 1; 1327, 1; 3571, 1; 10099, 1; 2127357527, 1; 7550870927, 1; 743712351035764423, 1
47^51+1 = [2, 4; 3, 2; 7, 1; 103, 1; 613, 1; 7039, 1; 216751, 1; 11048879, 1; 775862797, 1; 50246304977640328639, 1
38^54+1 = [5, 1; 17, 2; 73, 1; 577, 1; 6733, 1; 2083693, 1; 31966557661, 1; 174889487881, 1
18^68+1 = [113, 1; 929, 1; 6529, 1; 4942513, 1; 3670499942033, 1
28^59-1 = [3, 3; 1063, 1; 87134177825869551823, 1
28^59+1 = [29, 1; 709, 1; 62423, 1; 2357237985408057691, 1; 32838214266689135929, 1
44^52+1 = [41, 1; 113, 1; 809, 1; 100673, 1; 10306817, 1; 662209601, 1; 29858953764973737037041733001, 1
41^53-1 = [2, 3; 5, 1; 107, 1; 78160903, 1; 1285362831383, 1
41^53+1 = [2, 1; 3, 1; 7, 1; 46747, 1
24^62+1 = [577, 1; 1117, 1; 89621300725940655868216717, 1
30^58+1 = [17, 1; 53, 1; 233, 1; 1277, 1; 1038907789081, 1; 10740913221769, 1
19^67-1 = [2, 1; 3, 2; 588518621, 1; 1650922227287, 1; 24299939580826833879511, 1
19^67+1 = [2, 2; 5, 1; 122641223, 1; 1060719211, 1; 47852968968481, 1
48^51-1 = [13, 1; 47, 1; 181, 1; 3469, 1; 17137, 1; 1356350177521, 1; 597903848569921, 1; 4072835692996489, 1
48^51+1 = [7, 2; 37, 1; 61, 1; 103, 1; 307, 1; 919, 1; 1429, 1; 3385995061, 1; 15046928594194747, 1; 304237673259331993, 1
34^56+1 = [113, 1; 47441, 1; 37642417, 1; 18614617919369921, 1
13^77-1 = [2, 2; 3, 1; 23, 1; 419, 1; 859, 1; 18041, 1; 5229043, 1; 624958606550654822293, 1
13^77+1 = [2, 1; 7, 2; 29, 1; 22079, 1; 78947177, 1; 128011456717, 1
23^63-1 = [2, 1; 7, 2; 11, 1; 19, 1; 29, 1; 43, 1; 79, 1; 379, 1; 160651, 1; 170689, 1; 644869, 1; 5336717, 1; 7792003, 1; 408030421, 1; 978769387, 1
23^63+1 = [2, 3; 3, 3; 13, 2; 71, 1; 127, 1; 163, 1; 271, 1; 673, 1; 1117, 1; 2969, 1; 501161274307, 1; 3336613325137, 1; 22865554874031409, 1
15^73-1 = [2, 1; 7, 1
15^73+1 = [2, 4; 293, 1; 1607, 1
20^66+1 = [13, 1; 89, 1; 401, 1; 12277, 1; 72733, 1; 315481, 1; 1297693, 1; 7930693, 1; 170770770413, 1; 6881957521693, 1
22^64+1 = [28289, 1
39^54+1 = [2, 1; 37, 1; 109, 1; 613, 1; 761, 1; 9613, 1; 15013, 1; 2311921, 1; 545899989068281, 1
21^65-1 = [2, 2; 5, 2; 79, 1; 131, 1; 40841, 1; 189437, 1; 443431, 1; 516094151, 1
21^65+1 = [2, 1; 11, 1; 521, 1; 185641, 1; 7021471715414521, 1; 101619538800983513441, 1
14^75-1 = [11, 1; 13, 1; 31, 1; 211, 1; 1051, 1; 2851, 1; 3761, 1; 15511, 1; 110256001, 1; 758855846709601, 1
14^75+1 = [3, 2; 5, 3; 61, 1; 71, 1; 101, 1; 151, 1; 401, 1; 811, 1; 4001, 1; 1948981, 1; 1656843549451, 1; 106463872671151, 1; 10429823947688701, 1
45^52+1 = [2, 1; 401, 1; 5113, 1; 14801333702715041, 1; 558349069635422030890372117489, 1
42^53-1 = [41, 1; 107, 1; 18869, 1; 2969688024031, 1; 1313372442855743981, 1
42^53+1 = [43, 1; 743, 1; 47701, 1; 645329, 1; 31168559, 1; 15810572130737, 1; 402070443112853237, 1
17^70+1 = [2, 1; 5, 2; 29, 1; 281, 1; 21881, 1; 63541, 1; 5766433, 1; 100688449, 1; 348838692130131428210021, 1
37^55-1 = [2, 2; 3, 2; 11, 2; 41, 1; 2663, 1; 4271, 1; 16831, 1; 27611, 1; 325271, 1; 1336275931, 1; 1855860368209, 1
37^55+1 = [2, 1; 19, 1; 23, 1; 2069, 1; 1824841, 1; 3511033241, 1; 98389112119, 1; 478826530601, 1
29^59-1 = [2, 2; 7, 1; 11415793, 1; 64194072873983107981983523, 1
29^59+1 = [2, 1; 3, 1; 5, 1; 9677, 1; 134494159, 1
26^61-1 = [5, 2; 2441, 1; 12622609, 1; 136644408227, 1
26^61+1 = [3, 3; 1831, 1; 73853189, 1; 123457071655259, 1
46^52+1 = [521, 1; 3009553, 1; 4477457, 1; 32781677235598497149737, 1
35^56+1 = [2, 1; 113, 1; 337, 1; 449, 1; 22191649, 1
31^58+1 = [2, 1; 13, 1; 37, 1; 233, 1; 18329, 1; 646550190571213, 1
40^54+1 = [61, 1; 109, 1; 1601, 1; 4969, 1; 41941, 1; 81649, 1; 100549, 1; 6961681, 1; 16777215995904000001, 1
33^57-1 = [2, 5; 1123, 1; 3877, 1; 9007, 1; 60767517259, 1; 75999152791, 1; 4862490466531, 1; 29228473104019333, 1
33^57+1 = [2, 1; 7, 1; 17, 1; 151, 1; 229, 1; 2699, 1; 143261, 1; 49225733, 1; 23596244629, 1; 109840597331, 1
43^53-1 = [2, 1; 3, 1; 7, 1; 444853169, 1
43^53+1 = [2, 2; 11, 1; 107, 1; 2396723879629, 1; 223403759365757, 1
18^69-1 = [7, 3; 17, 1; 47, 1; 599, 1; 4831, 1; 7468009, 1; 20801237997245359, 1
18^69+1 = [19, 1; 139, 1; 307, 1; 3313, 1; 824418892380831861979, 1; 3913037558632733048069409307, 1
50^51-1 = [7, 2; 103, 1; 137, 1; 2551, 1; 43339993937, 1; 262231331604679, 1
50^51+1 = [3, 2; 17, 2; 19, 1; 43, 1; 33457, 1; 235402888003, 1; 373817122061401, 1; 5338225155840794744251, 1
28^60+1 = [41, 1; 601, 1; 7321, 1; 29201, 1; 41641, 1; 614657, 1; 51605161, 1; 7257822361, 1; 2863024493281, 1
13^78+1 = [2, 1; 5, 1; 17, 1; 313, 1; 1873, 1; 28393, 1; 380329, 1; 2874105113569, 1; 1418792215861230619657, 1
38^55-1 = [11, 2; 37, 1; 991, 1; 194681, 1; 224027, 1; 28781768489, 1; 1247726246121751293068161, 1
38^55+1 = [3, 1; 13, 1; 23, 1; 331, 1; 463, 1; 1123, 1; 156971, 1; 1545391, 1; 2031671, 1
47^52+1 = [2, 1; 97, 1; 25153, 1; 4612297, 1; 4726517464818819203167095821633, 1
24^63-1 = [19, 1; 23, 1; 29, 1; 43, 1; 239, 1; 601, 1; 2017, 1; 4987, 1; 28771, 1; 2585521, 1; 10426753, 1; 78066619, 1; 7851475297, 1
24^63+1 = [5, 2; 7, 2; 79, 1; 127, 1; 199, 1; 631, 1; 1009, 1; 5167, 1; 7561, 1; 12433, 1; 29863, 1; 183458857, 1; 433178719, 1; 3711692194858030321, 1
19^68+1 = [2, 1; 17, 2; 409, 1; 3833, 1; 29935777, 1; 2168875009642198021909889, 1
15^74+1 = [2, 1; 113, 1; 149, 1; 52987400285765657, 1; 16882057614458789568659053197037, 1
51^51-1 = [2, 1; 5, 2; 7, 1; 239, 1; 379, 1; 1259, 1; 6529, 1; 6733, 1; 403547, 1; 31695073, 1; 555154007, 1; 1716587581, 1; 8120815069, 1
51^51+1 = [2, 2; 13, 1; 103, 1; 307, 1; 2551, 1; 276319, 1; 154553257, 1; 154640443561, 1; 121116871999237, 1; 13292647508176547593, 1
41^54+1 = [2, 1; 13, 1; 29, 2; 109, 1; 397, 1; 433, 1; 1009, 1; 1993, 1; 4380589, 1; 12858553, 1
44^53-1 = [43, 1; 107, 1; 182639, 1; 54279739, 1; 45939298661, 1; 2956375229099640912752761, 1
44^53+1 = [3, 2; 5, 1; 23321, 1; 5246239663591, 1; 215078346901001, 1
14^76+1 = [41, 1; 937, 1
30^59-1 = [29, 1; 7583077905022163, 1; 8733964502075179, 1; 14198139768945840610067863, 1
30^59+1 = [31, 1; 269041, 1; 663968183, 1
23^64+1 = [2, 1; 1260241990896941895937, 1
20^67-1 = [19, 1; 906779, 1; 607366391, 1
20^67+1 = [3, 1; 7, 1; 269, 1; 155933666228489, 1
22^65-1 = [3, 1; 7, 1; 79, 1; 521, 1; 2003, 1; 245411, 1; 330331, 1; 85107437663, 1; 37987538607331, 1; 3198633375097421, 1
22^65+1 = [23, 1; 131, 1; 224071, 1; 3702791, 1; 59512246816751, 1; 1169669660009891, 1; 12296089473177511, 1
21^66+1 = [2, 1; 13, 1; 17, 1; 61, 1; 89, 1; 661, 1; 3181, 1; 724051700079313, 1; 4718573764413203147069, 1
34^57-1 = [3, 2; 11, 1; 397, 1; 6271, 1; 12541, 1; 575777, 1; 150586169165353, 1; 297141194226589, 1; 3748609209536524633, 1
34^57+1 = [5, 1; 7, 1; 1123, 1; 50506651087, 1; 421461812731, 1; 8497147335047089, 1; 1867518117232382203, 1
17^71-1 = [2, 4
17^71+1 = [2, 1; 3, 2; 6959, 1; 329853647, 1
48^52+1 = [15601, 1; 5308417, 1; 83853960863089, 1; 942499063408906797898417, 1
39^55-1 = [2, 1; 19, 1; 23, 1; 31, 1; 89, 1; 191, 1; 401, 1; 2531, 1; 1612564493, 1
39^55+1 = [2, 3; 5, 2; 11, 2; 12211, 1; 41011, 1; 47741, 1; 71232151, 1; 649979193601, 1; 16344485873101, 1
45^53-1 = [2, 2; 11, 1
45^53+1 = [2, 1; 23, 1; 107, 1; 12721, 1; 39715089823374481, 1; 224623416402142669, 1
42^54+1 = [5, 1; 37, 1; 109, 1; 353, 1; 673, 1; 4621, 1; 41966317, 1; 814309985977044589, 1; 242939258767771734529, 1
26^62+1 = [677, 1; 7193, 1; 706801, 1; 4833655657, 1; 16468551973, 1; 13493160747690157637, 1
29^60+1 = [2, 1; 41, 1; 241, 1; 9001, 1; 87121, 1; 353641, 1; 1593841, 1; 55576681, 1; 6103563899172302171321, 1
37^56+1 = [2, 1; 17, 1; 113, 1; 7118330801, 1; 103308219233, 1; 20655497029553, 1
18^70+1 = [5, 3; 13, 1; 29, 1; 281, 1; 1373, 1; 2801, 1; 15101, 1; 17837, 1; 145501, 1; 1623833, 1; 22576710941, 1; 29420891411500261, 1
31^59-1 = [2, 1; 3, 1; 5, 1; 125693727758648407613, 1
31^59+1 = [2, 5; 1048987974531167443121633837864965091749, 1
13^79-1 = [2, 2; 3, 1; 3793, 1; 16433, 1; 6709792556882923, 1
13^79+1 = [2, 1; 7, 1; 25202746699639, 1
35^57-1 = [2, 1; 13, 1; 17, 1; 97, 1; 131058353, 1; 110994071937949, 1; 48792067336049769437, 1
35^57+1 = [2, 2; 3, 3; 397, 1; 19609, 1; 13246687, 1; 265414653839119, 1; 455914145581257265993, 1
33^58+1 = [2, 1; 5, 1; 109, 1; 233, 2; 1277, 1; 15559931209, 1; 13359072262646035080724944841, 1
40^55-1 = [3, 1; 13, 1; 67, 1; 148721, 1; 910361, 1; 2625641, 1; 1079314963, 1; 34800349194161, 1; 86193242841822798001, 1
40^55+1 = [11, 3; 23, 1; 41, 1; 20641, 1; 3687047401291, 1; 444783032873807, 1; 28819072829090287811, 1
46^53-1 = [3, 2; 5, 1; 41341, 1; 697756643452794847, 1
46^53+1 = [47, 1; 107, 1; 1978597, 1; 30175127, 1; 192079967356758001, 1
15^75-1 = [2, 1; 7, 1; 11, 1; 61, 1; 241, 1; 4931, 1; 20101, 1; 46751, 1; 39225301, 1; 316091724098401, 1; 7112705843777290751, 1
15^75+1 = [2, 4; 31, 1; 151, 1; 211, 1; 1531, 1; 19231, 1; 44101, 1; 142111, 1; 712651, 1; 2080801, 1; 5062201, 1; 9555151, 1; 34800625873379851, 1
43^54+1 = [2, 1; 5, 2; 37, 1; 829, 1; 3416953, 1; 222980186914561, 1; 48202208432980957, 1
19^69-1 = [2, 1; 3, 3; 127, 1; 277, 1; 2347, 1; 1530559, 1; 9555459481, 1; 16497763013, 1; 1335495402823, 1; 71425475193776503, 1
19^69+1 = [2, 2; 5, 1; 7, 3; 47, 1; 139, 1; 691, 1; 2531, 1; 5521, 1; 34409530237, 1; 1552450817964462079, 1; 156832034288392140949, 1
14^77-1 = [13, 1; 67, 1; 3851, 1; 4027, 1; 59753, 1; 140449, 1; 1154539, 1; 8108731, 1; 53380217213346395075243, 1
14^77+1 = [3, 1; 5, 1; 23, 1; 56519, 1; 7027567, 1; 11737870057, 1; 293626525039, 1; 11201223484991, 1; 36707095599329, 1
28^61-1 = [3, 3; 584814157619, 1; 108152440326426913, 1
28^61+1 = [29, 1; 6101, 1; 11743477, 1; 109721921, 1
24^64+1 = [573569, 1; 21635329, 1; 609470977, 1; 4749538561, 1; 86970465821421497857, 1
50^52+1 = [97, 1; 7489, 1; 64433, 1; 1979734077579218689, 1
38^56+1 = [113, 1; 539089, 1; 8065073, 1; 23755649, 1; 461254585180157187328960488929, 1
20^68+1 = [137, 1; 2857, 1; 3673, 1; 160001, 1; 230734661278799273, 1; 2878870785836948026295038313, 1
23^65-1 = [2, 1; 11, 1; 911, 1; 31721, 1; 292561, 1; 4922971, 1; 47691619, 1; 480393499, 1
23^65+1 = [2, 3; 3, 1; 31, 1; 41, 1; 131, 1; 211, 1; 21001515080686141, 1
21^67-1 = [2, 2; 5, 1; 269, 1; 324363426169571, 1; 312929837239650768379490219650039, 1
21^67+1 = [2, 1; 11, 1; 278051, 1
17^72+1 = [2, 1; 18913, 1; 184417, 1; 7230961, 1; 48661191868691111041, 1
22^66+1 = [5, 1; 97, 1; 157, 1; 1321, 1; 1489, 1; 9617835527609, 1; 73194743542229, 1; 202786475872944559021009, 1
47^53-1 = [2, 1; 23, 1; 107, 1; 20429593, 1; 170950948322148276790648352651, 1
47^53+1 = [2, 4; 3, 1; 2976682673, 1
30^60+1 = [41, 1; 73, 1; 241, 1; 3361, 1; 12241, 1; 63361, 1; 9820801, 1; 8987660137, 1; 87335713721, 1
41^55-1 = [2, 3; 5, 2; 23, 1; 3631, 1; 132947, 1; 579281, 1; 38570071, 1; 4499415031, 1
41^55+1 = [2, 1; 3, 1; 7, 1; 11, 2; 61, 1; 2311, 1; 4111, 1; 18701, 1; 5914591, 1; 5669871130991, 1; 3965546268971820391, 1
44^54+1 = [13, 1; 109, 1; 149, 1; 1753, 1; 2137, 1; 53353, 1; 15776749, 1; 63101809, 1; 3337448720869, 1; 889247314335298801357, 1
51^52+1 = [2, 1; 73, 1; 313, 1; 46337, 1; 279137, 1; 38883213942350233, 1; 7455035733657197125961, 1
34^58+1 = [13, 1; 89, 1; 5032081, 1; 1076312344344269, 1
39^56+1 = [2, 1; 17, 1; 113, 1; 449, 1; 1009, 1; 3457, 1; 45534289, 1
48^53-1 = [47, 1; 107, 1; 9013085165975591837557, 1
48^53+1 = [7, 2; 385735606172209, 1; 1446050602074967789, 1
13^80+1 = [2, 1; 2657, 1; 441281, 1; 444641, 1; 4335041, 1; 283763713, 1; 1116130730334721, 1; 1266394281048641, 1
18^71-1 = [17, 1; 569, 1; 171677613761, 1; 23821298356519, 1; 8313279867213693856690162577, 1
18^71+1 = [19, 1; 5113, 1; 1206599617106390561, 1; 99988492874568924239703307744649, 1
26^63-1 = [5, 2; 19, 1; 37, 1; 127, 1; 337, 1; 90847, 1; 3083473, 1; 308933353, 1; 321272407, 1; 2997305809, 1; 25460272531, 1
26^63+1 = [3, 5; 7, 2; 31, 1; 43, 1; 71, 2; 211, 1; 43093, 1; 59011, 1; 1296037, 1; 11822077, 1; 102966067, 1; 1560259846741, 1
29^61-1 = [2, 2; 7, 1; 1831, 1; 13751019673, 1; 28004534179193290272271310975007581, 1
29^61+1 = [2, 1; 3, 1; 5, 1; 367, 1; 20884950575579566643, 1
52^52+1 = [89, 1; 82153, 1; 383969, 1; 94072729297, 1
45^54+1 = [2, 1; 13, 1; 37, 1; 1013, 1; 8521, 1; 157933, 1; 237277, 1; 1840016161, 1; 23839875721, 1; 17870950328293, 1
42^55-1 = [11, 2; 41, 1; 181, 1; 881, 1; 991, 1; 1601, 1; 2971, 1; 531922931, 1; 5942675707, 1
42^55+1 = [23, 3; 43, 1; 67, 1; 131, 1; 23201, 1; 618421, 1; 20465173367, 1
15^76+1 = [2, 1; 17, 1; 761, 1; 1489, 1; 7753, 1; 114001, 1
37^57-1 = [2, 2; 3, 3; 7, 1; 67, 1; 229, 1; 4413131, 1; 75203859636364813, 1; 3933538789573170812717, 1
37^57+1 = [2, 1; 19, 2; 31, 1; 43, 1; 191, 1; 53685451, 1; 8096700889, 1; 559698440382833, 1; 113486778854966833, 1
14^78+1 = [37, 1; 53, 1; 197, 1; 1033, 1; 140557, 1; 178616881, 1; 377069317, 1; 232815192715561, 1; 337803644207780297, 1
31^60+1 = [2, 1; 409, 1; 1129, 1; 35401, 1; 1546081, 1; 852890113921, 1; 727422334085254365392641, 1
19^70+1 = [2, 1; 29, 1; 181, 1; 421, 1; 5237, 1; 116895941, 1; 14533200697, 1; 16936647121, 1; 41921106691107421, 1
35^58+1 = [2, 1; 349, 1; 613, 1
33^59-1 = [2, 5; 625283, 1; 26637127099650245465999, 1
33^59+1 = [2, 1; 17, 1; 17481701, 1; 40458071, 1
24^65-1 = [23, 1; 53, 1; 6553, 1; 15913, 1; 346201, 1; 6895253, 1; 1679822951, 1
24^65+1 = [5, 3; 11, 1; 131, 1; 5791, 1; 33203, 1; 76831, 1; 104911, 1; 1317941, 1; 619691539831653045336579590501, 1
40^56+1 = [17, 2; 113, 1; 337, 1; 641, 1; 929, 1
28^62+1 = [5, 1; 157, 1; 17981, 1; 32660609, 1; 41183608552636142233, 1
20^69-1 = [19, 1; 139, 1; 421, 1; 691, 1; 1381, 1; 119553964489, 1; 113317059163579, 1; 46266279097921483078651, 1
20^69+1 = [3, 2; 7, 1; 47, 1; 127, 1; 461, 1; 967, 1; 563041, 1; 197317369, 1; 3274400525856244223, 1
46^54+1 = [13, 1; 29, 1; 73, 1; 344257, 1; 4416877, 1; 8375617, 1; 10717097219713, 1
17^73-1 = [2, 4; 293, 1; 1621745371, 1; 3038535503, 1; 319344640907, 1; 596137412912777, 1
17^73+1 = [2, 1; 3, 2; 284117, 1; 1517302254487813, 1
43^55-1 = [2, 1; 3, 1; 7, 1; 3500201, 1; 6038099, 1; 3664405207, 1; 4701988171, 1; 366423971294701, 1
43^55+1 = [2, 2; 11, 2; 23, 1; 67, 1; 359063, 1; 3341101, 1; 3470039, 1; 7545890441, 1
23^66+1 = [2, 1; 5, 1; 37, 1; 53, 1; 7549, 1; 924209309, 1; 1853387306082786629, 1
21^68+1 = [2, 1; 137, 1; 953, 1; 97241, 1; 2610929, 1; 2691707418840001, 1; 5357156372335908409, 1
22^67-1 = [3, 1; 7, 1; 1609, 1; 3159310638577, 1; 149975938430081, 1; 772984350552229340405744597, 1
22^67+1 = [23, 1; 1484803176334477, 1; 5892621097397450166023917042943, 1
50^53-1 = [7, 2; 743, 1; 1697, 1; 9973753, 1; 825025103671, 1; 272334912935459277200953, 1
50^53+1 = [3, 1; 17, 1; 107, 1; 14348939419, 1; 9911826142994299, 1; 4234603544656703361353843, 1
38^57-1 = [37, 1; 1483, 1; 946961, 1; 2730529, 1; 2472887089, 1; 5814949641992539, 1; 29604281041250521291043, 1
38^57+1 = [3, 2; 7, 1; 13, 1; 67, 1; 191, 1; 3079, 1; 25537, 1; 34388297791, 1; 2557253710679, 1; 15854528121577, 1; 54452339548543, 1
30^61-1 = [29, 1; 296217221, 1; 2935763471, 1; 6147298583195971, 1; 1811929227218224761617, 1
30^61+1 = [31, 1; 5754549342828866862470636001654375469235641, 1
13^81-1 = [2, 2; 3, 5; 61, 1; 650971, 1; 1609669, 1; 57583418699431, 1; 1102123844336048491, 1
13^81+1 = [2, 1; 7, 1; 19, 1; 157, 1; 163, 1; 271, 1; 937, 1; 30133, 1; 73387, 1; 904663, 1; 1094473, 1; 259640317, 1; 770321341, 1; 762615992953, 1
47^54+1 = [2, 1; 5, 1; 13, 1; 17, 1; 109, 1; 1153, 1; 1213, 1; 1621, 1; 2341, 1; 2377, 1; 4021, 1; 10909, 1; 43047067786381, 1
41^56+1 = [2, 1; 17, 1; 23633, 1; 30689, 1; 1945700849, 1; 234850742033, 1; 3165968065606081, 1; 1090658541704502389921, 1
34^59-1 = [3, 1; 11, 1; 763579, 1
34^59+1 = [5, 1; 7, 1; 14869, 1; 361336951504123657, 1; 5942770823154896362982945993, 1
18^72+1 = [97, 1; 577, 1; 1153, 1; 2474209, 1; 113607841, 1; 42569092513, 1; 994416129981667873, 1
44^55-1 = [43, 1; 3301, 1; 6337, 1; 3835261, 1; 12958962721, 1; 1818796420541, 1; 4391645526973, 1
44^55+1 = [3, 2; 5, 2; 23, 1; 89, 1; 421, 1; 991, 1; 1321, 1; 1741, 1; 3037, 1; 16061, 1; 2625811, 1; 4316489, 1; 439776041, 1; 24561393887581, 1
51^53-1 = [2, 1; 5, 2; 18029117, 1; 10081630639, 1; 57234982774399, 1; 3346107475207652130011, 1
51^53+1 = [2, 2; 13, 1; 107, 1; 1697, 1; 10909186637846333, 1
14^79-1 = [13, 1; 11289101, 1; 38775097, 1
14^79+1 = [3, 1; 5, 1; 160687, 1; 17428672520072491888720964879939, 1
26^64+1 = [257, 1; 5394435329, 1; 7796647730590584577, 1; 107248611633411791617, 1
15^77-1 = [2, 1; 7, 2; 67, 1; 463, 1; 2333, 1; 5237, 1; 8537, 1; 1743463, 1; 28095816025663, 1
15^77+1 = [2, 4; 23, 1; 4159, 1; 10678711, 1; 23504771357, 1; 96821654187863868183691, 1
29^62+1 = [2, 1; 421, 1; 2685097, 1; 1827530475629, 1
39^57-1 = [2, 1; 7, 1; 19, 2; 223, 1; 146681, 1; 106808885663, 1; 150213543013, 1; 1337171007589, 1
39^57+1 = [2, 3; 5, 1; 1483, 1; 7297, 1; 20749, 1; 83520733, 1; 88520264890723, 1; 69699377407912279, 1
48^54+1 = [5, 1; 73, 1; 461, 1; 34849, 1; 5306113, 1; 58800587853529, 1; 294676606848817, 1; 2115306485221840921, 1
19^71-1 = [2, 1; 3, 2; 17041, 1; 49417, 1; 19840332702980239, 1; 1367953340395774788360889, 1
19^71+1 = [2, 2; 5, 1; 2059828429, 1; 2666842361, 1; 27801690183630617, 1
42^56+1 = [113, 1; 2689, 1; 218401, 1; 2552816449, 1; 5538775313, 1; 85687185809, 1
45^55-1 = [2, 2; 11, 2; 89, 1; 881, 1; 1471, 1; 2851, 1; 34211, 1; 10695631, 1; 35341681, 1; 789398501, 1; 35571508524949, 1; 189042704081237051, 1
45^55+1 = [2, 1; 23, 1; 41, 1; 67, 1; 97841, 1; 497170117203343, 1; 102816644479677642158921, 1
52^53-1 = [3, 1; 17, 1; 107, 1
52^53+1 = [53, 2; 181194015068926422899222020415627, 1
37^58+1 = [2, 1; 5, 1; 137, 1; 188862267838638894183617588461, 1
31^61-1 = [2, 1; 3, 1; 5, 1; 14519, 1; 50848444051, 1; 12712081567468100953, 1; 13578586277937589671409, 1
31^61+1 = [2, 5; 977, 1; 60290903116166148697, 1
17^74+1 = [2, 1; 5, 1; 29, 1; 194296461049, 1; 1017719645617, 1; 1649702304713, 1; 3805112685822988789997017, 1
20^70+1 = [41, 1; 197, 1; 281, 2; 401, 1; 2801, 1; 14561, 1; 140281, 1; 222361, 1; 1424354653, 1; 13428508670641, 1; 608569597978252121, 1
24^66+1 = [13, 1; 73, 1; 349, 1; 577, 1; 1321, 1; 11617, 1; 212917, 1; 4666069, 1; 261501808988233731193, 1; 522913580874289935529, 1
35^59-1 = [2, 1; 17, 1; 4603, 1; 128960549, 1; 2322377756400939037, 1
35^59+1 = [2, 2; 3, 2; 24781, 1; 18545117, 1; 1111584191, 1; 44865317981742568759439, 1
33^60+1 = [2, 1; 97, 1; 521, 1; 6113, 1; 15313, 1; 807281, 1; 91844017, 1; 4702840151252041, 1; 555357410666628001, 1
28^63-1 = [3, 5; 19, 2; 113, 1; 271, 1; 1009, 1; 444979, 1; 4422461, 1; 223934956756993189, 1; 154154940307497300453157, 1
28^63+1 = [29, 1; 37, 1; 43, 1; 127, 1; 631, 1; 757, 1; 2269, 1; 13007, 1; 29443, 1; 35771, 1; 102547, 1; 132679, 1; 546211, 1; 1905121, 1; 164630467, 1; 1994659633, 1; 28927311337, 1
21^69-1 = [2, 2; 5, 1; 47, 1; 463, 1; 19597, 1; 459878292118921111, 1; 139870566115103282847737, 1
21^69+1 = [2, 1; 11, 1; 139, 1; 277, 1; 421, 1; 461, 1; 599, 1; 691, 1; 2215825387044753577, 1
23^67-1 = [2, 1; 11, 1; 269, 1; 2152900439563539121, 1
23^67+1 = [2, 3; 3, 1
22^68+1 = [73, 1; 3209, 1; 27385777, 1; 132928441, 1
40^57-1 = [3, 2; 13, 1; 547, 1; 62929, 1; 52960639, 1; 5071725282008449, 1; 70481514601025641025641025641, 1
40^57+1 = [7, 1; 41, 1; 223, 1; 419, 1; 1597, 1; 100192921300171974614927, 1
13^82+1 = [2, 1; 5, 1; 17, 1; 1089083758501, 1; 1508425553233, 1
53^53-1 = [2, 2; 13, 1; 107, 1; 141829, 1; 16505521259654533, 1; 143470720478589313288313473, 1
53^53+1 = [2, 1; 3, 3; 991313, 1; 2644277, 1; 5324593, 1; 14443842647093, 1; 19604216783737, 1
46^55-1 = [3, 2; 5, 2; 727, 1; 1409, 1; 9901, 1; 181787, 1; 232871, 1; 253661, 1; 915391, 1; 9425043975161, 1
46^55+1 = [11, 2; 31, 1; 47, 1; 71, 1; 181, 1; 661, 1; 991, 1; 12211, 1; 399719, 1; 104811719, 1; 1805718764081, 1; 2223777861466481, 1
43^56+1 = [2, 1; 113, 1; 3713921, 1; 7155121, 1; 5844100138801, 1; 857869846157969, 1
30^62+1 = [17, 1; 53, 1; 1028333, 1; 28722878633, 1; 11974742836578872916206719364929, 1
38^58+1 = [5, 1; 17, 2; 349, 1; 4177, 1
18^73-1 = [17, 1; 439, 1; 239879, 1; 846217, 1; 118874953, 1
18^73+1 = [19, 1
14^80+1 = [193, 1; 641, 1; 14401, 1; 32801, 1; 11284732320255809, 1; 117686299357503737281, 1
15^78+1 = [2, 1; 13, 2; 113, 1; 157, 1; 3877, 1; 11909, 1; 15289, 1; 15601, 1; 16433, 1; 18617, 1; 30313817, 1; 151747597, 1; 12833766874934773, 1
50^54+1 = [13, 1; 37, 1; 41, 1; 61, 1; 73, 1; 109, 1; 157, 1; 3061, 1; 5761801, 1; 15687625501, 1; 1748306798101261, 1; 2181938199770341, 1
34^60+1 = [41, 1; 1321, 1; 74521, 1; 1336337, 1; 6220385881, 1; 9465822281, 1; 1785792568561, 1; 243489425809747617001, 1
41^57-1 = [2, 3; 5, 1; 1723, 1; 8209, 1; 12541, 1; 8836483, 1; 87423871753, 1; 100200775387183, 1; 3291273019692283, 1
41^57+1 = [2, 1; 3, 2; 7, 1; 191, 1; 547, 1; 571, 1; 2573209, 1; 83306471920220930893, 1; 547785610778958259612376471, 1
47^55-1 = [2, 1; 11, 2; 23, 1; 31, 1; 14621, 1; 134707, 1; 495622931, 1; 398959160491, 1
47^55+1 = [2, 4; 3, 1; 389357, 1; 4778021, 1; 15760471, 1; 132277876039, 1
26^65-1 = [5, 3; 11, 1; 8641, 1; 10271, 1; 27764777, 1; 3574533119, 1; 7106335471, 1; 161404898442841, 1
26^65+1 = [3, 3; 131, 1; 431, 1; 521, 1; 937, 1; 1021, 1; 6449, 1; 38299, 1; 397073, 1; 255692934121, 1; 50815915796881, 1; 143608105465241, 1
44^56+1 = [17, 1; 241, 1; 449, 1; 1009, 1; 3457, 1; 991873, 1; 2300965548823537, 1; 11877622714413569, 1; 684164473040964833, 1
19^72+1 = [2, 1; 241, 1; 577, 1; 1009, 1; 4657, 1; 14929, 1; 15073, 1; 29569, 1; 563377, 1; 7957659850849, 1; 221901363412892497, 1
29^63-1 = [2, 2; 7, 2; 13, 1; 67, 1; 6637, 1; 14437, 1; 41203, 1; 88009573, 1; 51473298317533, 1; 52012313485270741, 1
29^63+1 = [2, 1; 3, 3; 5, 1; 19, 1; 43, 1; 127, 1; 271, 1; 379, 1; 1035469, 1; 10435069, 1; 574995877, 1; 8220076663, 1; 68630611242149057557, 1
51^54+1 = [2, 1; 37, 1; 109, 1; 1301, 1; 182773, 1; 309629344358025127801, 1; 7568656507911929318087257, 1
39^58+1 = [2, 1; 349, 1; 761, 1; 6061697, 1; 1616210112221, 1; 33099537219253, 1
17^75-1 = [2, 4; 151, 1; 307, 1; 2551, 1; 5101, 1; 5351, 1; 88741, 1; 26278001, 1; 6566760001, 1; 11330289301, 1; 1995937064371951, 1
17^75+1 = [2, 1; 3, 3; 7, 1; 11, 1; 13, 1; 31, 1; 71, 1; 101, 1; 2851, 1; 238212511, 1; 2414909984054562151, 1; 4064228544226537005066401, 1
20^71-1 = [19, 1; 201161092255316201234202042361, 1
20^71+1 = [3, 1; 7, 1; 569, 1; 3068721247, 1; 3389724375173873063832460218247, 1
13^83-1 = [2, 2; 3, 1; 12451, 1; 1383113, 1
13^83+1 = [2, 1; 7, 1; 167, 1; 499, 1
31^62+1 = [2, 1; 13, 1; 37, 1; 415153, 1
48^55-1 = [11, 2; 23, 1; 47, 1; 541, 1; 911, 1; 39359, 1; 73245991369, 1; 133346010356326028004534788938271, 1
48^55+1 = [7, 2; 2311, 1; 3631, 1; 233641, 1; 5200081, 1; 10222411, 1; 17515852613887, 1; 28224390310692207088269781, 1
24^67-1 = [23, 1; 269, 1; 96677174494301, 1
24^67+1 = [5, 2; 140633939, 1; 2853572850064208346290342691280609, 1
37^59-1 = [2, 2; 3, 2; 1065262887626860537583, 1
37^59+1 = [2, 1; 19, 1; 673781, 1; 1048366055338267, 1; 118930771686451557373, 1
42^57-1 = [13, 1; 41, 1; 139, 1; 229, 1; 457, 1; 4523, 1; 1482402079, 1; 241439529047, 1
42^57+1 = [43, 1; 1723, 1; 15277, 1; 23029, 1; 1531094329, 1; 455459569835623, 1; 10573773017297431501875439, 1
21^70+1 = [2, 1; 13, 1; 17, 1; 29, 1; 41, 1; 3697, 1; 50261, 1; 4325861, 1; 920421641, 1; 68454248717, 1; 92152520881, 1
45^56+1 = [2, 1; 17, 1; 113, 1; 494562511489, 1
23^68+1 = [2, 1; 137, 1; 139921, 1; 283162745757740538620032064126776401913969, 1
28^64+1 = [9473, 1; 836609, 1; 1750913, 1; 33056264688182274910972033, 1
22^69-1 = [3, 2; 7, 1; 13, 2; 4463, 1; 1323064018651, 1; 60575166785239, 1
22^69+1 = [23, 2; 47, 1; 139, 1; 277, 1; 461, 1; 463, 1; 1381, 1; 1933, 1; 176227, 1; 245494445849562491, 1; 9552007992825634081, 1
33^61-1 = [2, 5; 8545613, 1; 24461333167483, 1; 728894223505535436867383800009, 1
33^61+1 = [2, 1; 17, 1; 353384347, 1; 4481450375424591159680464717, 1
35^60+1 = [2, 1; 41, 1; 401, 1; 761, 1; 2441, 1; 3761, 1; 5737, 1; 9601, 1; 750313, 1; 4598201, 1; 392517673, 1; 111194154961, 1
52^54+1 = [5, 1; 37, 1; 109, 1; 541, 1; 7308913, 1; 2290013533, 1; 2371258261, 1; 4648485432457, 1; 10564243418012961709, 1
14^81-1 = [13, 1; 163, 1; 211, 1; 397, 1; 4861, 1; 18973, 1; 854582077, 1; 1427145211, 1; 299113818931, 1
14^81+1 = [3, 5; 5, 1; 19, 1; 61, 1; 1459, 1; 132049, 1; 2884897, 1; 1177426963, 1; 120850766857, 1; 789080627989, 1; 69205137817155935977, 1
18^74+1 = [5, 2; 13, 1; 149, 1; 1481, 1; 3257, 1; 245916653, 1; 2790448537, 1; 10763275729, 1; 647596604061431090273, 1
15^79-1 = [2, 1; 7, 1; 317, 1; 289141, 1
15^79+1 = [2, 4; 7113319, 1; 46872275419, 1; 102274698919, 1; 8508107485100663161, 1; 62117692148169172283, 1
40^58+1 = [1601, 1; 74435461, 1; 13376719841263353095343548507171021, 1
30^63-1 = [7, 3; 19, 1; 29, 1; 71, 1; 113, 1; 127, 1; 379, 1; 93997, 1; 116047, 1; 729027001, 1; 73392189661173853, 1
30^63+1 = [13, 1; 31, 1; 37, 1; 43, 1; 67, 1; 163, 1; 631, 1; 36037, 1; 120871, 1; 1118041, 1; 10214359, 1; 1250258563, 1
43^57-1 = [2, 1; 3, 2; 7, 1; 229, 1; 631, 1; 2699, 1; 4219, 1; 4789, 1; 46399, 1; 1849563931, 1; 2137444528747943, 1; 5364496730517951157, 1
43^57+1 = [2, 2; 11, 1; 13, 1; 139, 1; 790819, 1; 246858439628645832157006697407, 1
53^54+1 = [2, 1; 5, 1; 109, 1; 281, 1; 1153, 1; 1621, 1; 6841, 1; 16453, 1; 18419690246401, 1
46^56+1 = [17, 1; 113, 1; 929, 1; 5792081, 1; 1269398609, 1
38^59-1 = [37, 1; 1063, 1; 1181, 1; 12037, 1; 46021, 1; 1894609, 1
38^59+1 = [3, 1; 13, 1; 13018462432992822178052993720857, 1
19^73-1 = [2, 1; 3, 2; 893943109, 1; 109796425517837, 1; 391818505243975817655620850033223, 1
19^73+1 = [2, 2; 5, 1; 1168845771004542397619, 1; 2603189638448754530124997, 1
26^66+1 = [181, 1; 677, 1; 2521, 1; 11518277, 1; 648056861, 1; 2665780306333, 1
34^61-1 = [3, 1; 11, 1; 22937, 1; 2214379423, 1; 480996815213, 1
34^61+1 = [5, 1; 7, 1; 977, 1; 8595023, 1; 1937783707, 1; 12066103736081, 1; 894918334993191527, 1; 486463673172169891637, 1
50^55-1 = [7, 2; 23, 1; 991, 1; 1871, 1; 49391, 1; 73679, 1; 110441, 1; 6377551, 1; 59337433, 1; 618387881, 1; 6804382065416431, 1
50^55+1 = [3, 1; 11, 2; 17, 1; 89, 1; 2531, 1; 131561, 1; 557041, 1; 81046630487681, 1; 1075746309759859, 1
17^76+1 = [2, 1; 41761, 1; 11355003629541687711335762857918877977, 1
41^58+1 = [2, 1; 29, 3; 5801, 1; 873133, 1; 17629681, 1; 252817284224865523775654613793, 1
54^54+1 = [13, 1; 37, 1; 73, 1; 109, 1; 313, 1; 577, 1; 2089, 1; 2917, 1; 7669, 1; 9181, 1; 83701, 1; 43238197, 1; 216500532402833926227361, 1
13^84+1 = [2, 1; 113, 1; 14281, 1; 815702161, 1; 213867479113, 1; 2341071239305009, 1; 4803378460849459680406337, 1
29^64+1 = [2, 1; 257, 1; 641, 1; 7937, 1; 19289729, 1; 63739777, 1; 162858237363862164959617, 1
47^56+1 = [2, 1; 113, 1; 68141473, 1; 388975441, 1; 3754832453681, 1; 11905643330881, 1
20^72+1 = [17, 1; 1873, 1; 8900929, 1; 675796129, 1; 1505882353, 1; 969759919969, 1
44^57-1 = [7, 1; 43, 1; 229, 2; 283, 1; 1177621, 1; 121954879987, 1; 6330760607333186161, 1
44^57+1 = [3, 3; 5, 1; 631, 1; 6689, 1; 96787, 1; 55850510034912951239060741, 1
24^68+1 = [137, 1; 28697, 1; 331777, 1; 13961078641, 1; 138814016717177, 1
39^59-1 = [2, 1; 19, 1; 54741499, 1; 1184471021, 1
39^59+1 = [2, 3; 5, 1; 362647729469645531483708582635843944440410721, 1
21^71-1 = [2, 2; 5, 1; 493509073, 1; 6912925952086714539251625713, 1
21^71+1 = [2, 1; 11, 1; 826880829487, 1; 172132091765842074983, 1
51^55-1 = [2, 1; 5, 3; 41, 2; 821, 1; 991, 1; 61395401, 1; 1977725861, 1; 231780662895871, 1; 7452207143911091, 1
51^55+1 = [2, 2; 11, 2; 13, 1; 23, 1; 17293, 1; 25147, 1; 60611, 1; 603191, 1; 11673047, 1
31^63-1 = [2, 1; 3, 3; 5, 1; 43, 1; 127, 1; 331, 1; 3637, 1; 6301, 1; 70309, 1; 81343, 1; 917087137, 1; 75077698123, 1; 2813432694367, 1
31^63+1 = [2, 5; 7, 3; 19, 1; 211, 1; 577, 1; 2143, 1; 11971, 1; 71821, 1; 1538083, 1; 45376431752737, 1; 550469850411853, 1; 1652484831253806817, 1
23^69-1 = [2, 1; 7, 1; 11, 1; 79, 1; 277, 1; 461, 1; 1289, 1; 1933, 1; 11593, 1; 831603031789, 1; 1920647391913, 1; 49696373692116337, 1
23^69+1 = [2, 3; 3, 2; 13, 2; 47, 1; 139, 1; 691, 1; 1013, 1; 7591, 1; 1641281, 1; 52626071, 1; 1522029233, 1; 643983069241, 1; 4027959480116314753, 1
22^70+1 = [5, 2; 97, 1; 181, 1; 401, 1; 4481, 1; 55441, 1; 83273, 1; 150901, 1; 34379269, 1; 66068941261, 1; 816048655801, 1; 892792661763983821, 1
14^82+1 = [197, 1; 1979317, 1; 117872082254721001, 1
28^65-1 = [3, 3; 53, 1; 131, 1; 637421, 1; 72416371, 1; 4543753614603737, 1; 90216355836698261, 1
28^65+1 = [11, 1; 29, 1; 547, 1; 2237, 1; 53951, 1; 114661, 1; 1598039, 1; 115508406521, 1
15^80+1 = [2, 1; 257, 1; 41281, 1; 885591361, 1; 12779004583099009, 1; 564643374177456961, 1
37^60+1 = [2, 1; 89, 1; 10529, 1; 3512477579761, 1; 289164210765572956376401, 1; 12337505331268672999818721, 1
18^75-1 = [7, 3; 17, 1; 31, 1; 41, 1; 151, 1; 601, 1; 2711, 1; 558721, 1; 602401, 1; 106487551, 1; 78180455401, 1; 21162386787273369601, 1
18^75+1 = [11, 1; 19, 1; 307, 1; 9041, 1; 130651, 1; 136651, 1; 738851, 1; 11630180251, 1; 17254127651933924651, 1
33^62+1 = [2, 1; 5, 1; 109, 1; 373, 1; 101681, 1; 11508831798337, 1; 48287631687301, 1
42^58+1 = [5, 1; 353, 1
48^56+1 = [17, 1; 113, 1; 184913, 1; 14669068417, 1; 3673834143379637783333671969, 1
35^61-1 = [2, 1; 17, 1; 2005847011022203920677223924210612017, 1
35^61+1 = [2, 2; 3, 2; 367, 1; 12323, 1; 143107, 1; 458599, 1; 1653101, 1
45^57-1 = [2, 2; 11, 1; 19, 2; 109, 1; 585578449280908796570517800071, 1
45^57+1 = [2, 1; 7, 1; 23, 1; 229, 1; 283, 1; 1483, 1; 62549, 1; 2140807, 1; 2820596041428749, 1
52^55-1 = [3, 1; 17, 1; 23, 1; 311, 1; 15401, 1; 23971, 1; 416092460939, 1; 676471825850591, 1; 166465035529146026971, 1
52^55+1 = [11, 2; 53, 1; 61, 1; 67, 1; 331, 1; 10691, 1; 16722605110751, 1; 2116830613728799, 1; 2468635613076398059409611, 1
40^59-1 = [3, 1; 13, 1; 4013, 1; 1183077323, 1; 13415463873849056807213, 1
40^59+1 = [41, 1; 1547453, 1; 188764040334851, 1; 1070111457289937336107279568567, 1
30^64+1 = [3102977, 1; 1015884157773292417, 1; 41439385338098953729, 1
19^74+1 = [2, 1; 181, 1; 593, 1; 1009361, 1; 3849970177, 1; 19406602558617444383054581, 1
13^85-1 = [2, 2; 3, 1; 103, 1; 443, 1; 30941, 1; 28152511, 1; 15798461357509, 1; 11435433293542010176161611, 1
13^85+1 = [2, 1; 7, 1; 11, 1; 1361, 1; 2411, 1; 617886851384381281, 1
43^58+1 = [2, 1; 5, 2; 37, 1
17^77-1 = [2, 4; 25646167, 1; 2141993519227, 1
17^77+1 = [2, 1; 3, 2; 23, 1; 947, 1; 22796593, 1; 87415373, 1
46^57-1 = [3, 3; 5, 1; 7, 1; 103, 1; 50047, 1; 13557679615951, 1; 869333244926326187979597262939, 1
46^57+1 = [19, 2; 47, 1; 109, 1; 229, 1; 1483, 1; 1597, 1; 41269, 1; 516877, 1; 8718949, 1; 77983645297, 1; 18109127427493, 1
38^60+1 = [41, 1; 409, 1; 1201, 1; 4201, 1; 4441, 1; 18217, 1; 50857, 1; 74161, 1; 583537, 1; 3058466641, 1; 4499711357732458971721, 1
26^67-1 = [5, 2; 4691, 1; 2728777, 1; 28661603960447, 1; 57073588142876873, 1
26^67+1 = [3, 3; 582693641, 1
53^55-1 = [2, 2; 11, 2; 13, 1; 131, 1; 5581, 1; 178250690949465223, 1
53^55+1 = [2, 1; 3, 3; 23, 1; 67, 1; 2011, 1; 3851, 1; 1354343, 1; 82244999, 1; 133372581761, 1
34^62+1 = [13, 1; 89, 1; 30133, 1; 44021, 1; 16927861, 1; 141048406381633206084256734073353889, 1
20^73-1 = [19, 1; 92419, 1; 6412324721641, 1
20^73+1 = [3, 1; 7, 1; 30223, 1; 80447, 1; 8140523, 1; 2991402761, 1; 5080516670789273543, 1
29^65-1 = [2, 2; 7, 1; 521, 1; 148123, 1; 732541, 1; 4748492087, 1; 118273570956941791, 1; 16132770616289764711, 1
29^65+1 = [2, 1; 3, 1; 5, 2; 11, 1; 31, 1; 53, 1; 131, 1; 401, 1; 1301, 1; 3407, 1; 5981, 1; 7489, 1; 24571, 1; 252918667, 1; 8704694974608881, 1
14^83-1 = [13, 1; 167, 1; 5479, 1; 19423, 1; 2802911, 1; 8692591, 1; 116910503156118431205311406881, 1
14^83+1 = [3, 1; 5, 1; 18427, 1; 45319, 1; 22722096794779061445351332313569, 1
50^56+1 = [193, 1; 60257, 1; 461847233, 1; 202396373057, 1; 19667981294391809, 1; 338026909819401601, 1
41^59-1 = [2, 3; 5, 1; 3659, 1; 181721, 1; 199083701, 1; 2847621359767557919841, 1
41^59+1 = [2, 1; 3, 1; 7, 1; 13003324711223675162020886035234448231, 1
21^72+1 = [2, 1; 193, 1; 433, 1; 673, 1; 62897, 1; 300673, 1; 1001713, 1; 25392481, 1; 4116371120264449, 1
24^69-1 = [23, 2; 47, 1; 139, 1; 601, 1; 124799, 1; 304751, 1; 502514966805721, 1; 58769065453824529, 1
24^69+1 = [5, 2; 7, 1; 79, 1; 98809, 1; 1397136559673839, 1; 22496867303759173834520497, 1
15^81-1 = [2, 1; 7, 1; 109, 1; 163, 1; 241, 1; 541, 1; 21061, 1; 16354441, 1; 829049498029, 1
15^81+1 = [2, 4; 19, 1; 211, 1; 739, 1; 811, 1; 355591, 1; 43448239, 1; 1477891879996957031251, 1
54^55-1 = [23, 1; 53, 1; 71, 1; 122021, 1; 23241461, 1; 9339586579414037, 1
54^55+1 = [5, 2; 11, 2; 31, 1; 3631, 1; 53861, 1; 530641, 1; 18818109157530101, 1
47^57-1 = [2, 1; 23, 1; 37, 1; 61, 1; 419, 1; 93498583, 1; 65247271367, 1; 46808539630950829, 1; 14397296085598887763, 1
47^57+1 = [2, 4; 3, 2; 7, 1; 103, 1; 571, 1; 1226360244664155943905473409283, 1
22^71-1 = [3, 1; 7, 1; 853, 1; 1333807, 1; 22769098493537073593, 1
22^71+1 = [23, 1; 12071, 1
44^58+1 = [13, 1; 149, 1; 5401865082113, 1; 4830846294099437, 1
23^70+1 = [2, 1; 5, 2; 53, 1; 61, 1; 701, 1; 941, 1; 10781, 1; 96601, 1; 272341, 1; 598193, 1; 3391669, 1; 1434849920564332861, 1
18^76+1 = [113, 1; 929, 1; 3539777, 1
31^64+1 = [2, 1; 257, 1; 641, 1; 2689, 1; 9601, 1; 13768516609, 1; 17777097601059636481, 1; 7231746495781123585793, 1
39^60+1 = [2, 1; 1156721, 1; 5352006947041, 1; 98477949003961, 1; 27653409549409201, 1; 301286680130415504601, 1
28^66+1 = [5, 1; 13, 1; 157, 1; 27017, 1; 47221, 1; 135433, 1; 23946685543873549601, 1
51^56+1 = [2, 1; 449, 1; 276750433, 1; 22883972285201, 1
37^61-1 = [2, 2; 3, 2; 1237300943, 1; 329526175817, 1
37^61+1 = [2, 1; 19, 1; 1709, 1; 238267, 1; 142937153, 1
33^63-1 = [2, 5; 37, 1; 379, 1; 421, 1; 463, 1; 631, 1; 1123, 1; 3163483, 1; 34905511, 1; 309521521, 1; 3317003886673, 1; 5536114346953, 1
33^63+1 = [2, 1; 7, 2; 17, 1; 19, 1; 29, 1; 43, 1; 127, 1; 151, 1; 197, 1; 211, 1; 307, 1; 19531, 1; 219409, 1; 221401, 1; 10907947, 1; 143436432637, 1; 8746792806277, 1; 734307341342527, 1
55^55-1 = [2, 1; 3, 3; 23, 1; 211, 1; 463, 1; 44171, 1; 4721201, 1; 2348047917161, 1; 24226294794769, 1
55^55+1 = [2, 3; 7, 1; 881, 1; 4011349, 1; 8987221, 1; 4378556711, 1; 62017050679, 1; 108447251221, 1; 32721931437361, 1; 49852934639531, 1
35^62+1 = [2, 1; 613, 1; 6664269889, 1; 3669026207719481442068577030169696656277, 1
42^59-1 = [41, 1; 6491, 1; 27967, 1
42^59+1 = [43, 1; 3541, 1; 41183, 1; 2823269, 1; 747270440711, 1
13^86+1 = [2, 1; 5, 1; 17, 1; 2753, 1; 748717, 1; 3605871444392247654973, 1; 14704313671678643430446722121, 1
48^57-1 = [13, 1; 47, 1; 181, 1; 229, 1; 39166598329, 1; 1868467947605686541562499217713, 1
48^57+1 = [7, 2; 37, 1; 61, 1; 1483, 1; 25309, 1; 1666111, 1; 45292771, 1; 6632395513, 1; 16014502657519, 1; 357858526401848657749, 1
45^58+1 = [2, 1; 1013, 1; 2089, 1; 177481, 1; 443237, 1; 10157059076413, 1; 656988022380357443330197, 1
19^75-1 = [2, 1; 3, 3; 31, 1; 101, 1; 127, 1; 151, 1; 211, 1; 911, 1; 1601, 1; 6451, 1; 2460181, 1; 6229677151, 1; 36035657195482151, 1; 164375644290642589501, 1
19^75+1 = [2, 2; 5, 3; 7, 3; 11, 1; 61, 1; 271, 1; 2251, 1; 79151, 1; 127051, 1; 467101, 1; 1081291, 1; 747596648084101, 1
17^78+1 = [2, 1; 5, 1; 29, 1; 83233, 1; 19825313, 1; 33610669, 1; 1224199237, 1; 13938043025453, 1
30^65-1 = [29, 1; 911, 1; 5851, 1; 13339, 1; 59281, 1; 178907, 1; 252877, 1; 837931, 1; 135905582691841, 1; 400650121113389033862431, 1
30^65+1 = [11, 1; 31, 1; 131, 1; 547, 1; 1301, 1; 71261, 1; 207169, 1; 799777421, 1; 4538397397, 1; 468284941714112167321, 1
52^56+1 = [977, 1; 54718248241, 1; 5069927558417, 1
40^60+1 = [769, 1; 3329, 1; 202481, 1; 34095552961, 1; 42160962241, 1; 298756141921, 1; 6553597440001, 1; 4295312810772302881, 1
26^68+1 = [17, 2; 137, 1; 26881, 1; 148921, 1; 13457627041, 1; 4909650468357640736849, 1
14^84+1 = [41, 1; 337, 1; 673, 1; 937, 1; 1009, 1; 774929, 1; 1475750641, 1; 1908233583265468033, 1; 4110630794871608561, 1
20^74+1 = [401, 1; 61244289678958373462403771583536382996866287437, 1
38^61-1 = [37, 1; 15739, 1
38^61+1 = [3, 1; 13, 1; 367, 1; 7321, 1; 17408260052741, 1; 58371947090011, 1; 7802043670722721331, 1
43^59-1 = [2, 1; 3, 1; 7, 1; 22067, 1; 988205107174469, 1; 6549070656905979504778461434303, 1
43^59+1 = [2, 2; 11, 1; 26147589158960053404590254331, 1
15^82+1 = [2, 1; 113, 1; 138583022521, 1; 30839158009109, 1; 1543059974108956456650786169201, 1
46^58+1 = [29, 2; 73, 1; 141637, 1
34^63-1 = [3, 3; 11, 1; 37, 1; 127, 1; 211, 1; 397, 1; 463, 1; 3437617, 1; 13917511, 1; 51200353, 1; 30785593609, 1; 10977681387665581, 1
34^63+1 = [5, 1; 7, 2; 19, 1; 29, 1; 43, 1; 71, 1; 109, 1; 1123, 1; 104119, 1; 745903, 1; 28072816507, 1; 57129000606695137, 1; 30822165800142669793, 1
29^66+1 = [2, 1; 37, 1; 61, 1; 313, 1; 421, 1; 285781, 1; 2294689, 1; 21437329, 1; 80484493, 1; 402546025333, 1; 439165605149799397, 1
21^73-1 = [2, 2; 5, 1; 30661, 1
21^73+1 = [2, 1; 11, 1; 293, 1; 439, 1; 877, 1; 1607, 1; 8303167, 1; 9428689079641451, 1; 1427364308750988577, 1
53^56+1 = [2, 1; 7057, 1; 226129, 1; 280673, 1; 394577, 1; 31129845205681, 1; 126419913004689137, 1; 24654928373305592994017, 1
24^70+1 = [61, 1; 577, 1; 97238233, 1; 374925097, 1; 1801385941, 1
22^72+1 = [17, 1; 241, 1; 2017, 1; 940993, 1; 4732993, 1; 3227992561, 1; 13278819202897, 1; 2112081624934238187268993, 1
18^77-1 = [17, 1; 23, 1; 199, 1; 449, 1; 463, 1; 16127, 1; 51217, 1; 80207, 1
18^77+1 = [19, 1; 536801, 1; 6301307, 1; 32222107, 1; 554461601, 1; 8575134569, 1
23^71-1 = [2, 1; 11, 1; 2131, 1; 351156543156995844791, 1; 12689965311931555366531418920750153, 1
23^71+1 = [2, 3; 3, 1; 353245517860142207052022009, 1
41^60+1 = [2, 1; 137, 1; 241, 1; 6121, 1; 10313, 1; 86161, 1; 156241, 1; 321961, 1; 432121, 1; 18478441, 1; 391810481, 1; 110312844281, 1
50^57-1 = [7, 2; 2551, 1; 30553, 1; 170887, 1; 3961952353, 1; 41958116255687, 1; 9483012119222263, 1; 92772235209725273, 1
50^57+1 = [3, 2; 17, 1; 19, 2; 43, 1; 457, 1; 3307, 1; 94849, 1; 160817, 1; 14601045331, 1; 31969257577, 1; 113138753154769, 1; 15387836214379711097, 1
13^87-1 = [2, 2; 3, 2; 61, 1; 1973, 1; 2843, 1; 3539, 1; 8527, 1; 846041103974872866961, 1; 808648601294417626878199, 1
13^87+1 = [2, 1; 7, 1; 59, 1; 157, 1; 1741, 1; 45353101, 1; 8546789918171, 1; 16397414286709, 1; 388719701504541540919, 1
31^65-1 = [2, 1; 3, 1; 5, 2; 11, 1; 911, 1; 1951, 1; 17351, 1; 42407, 1; 2426789, 1; 7908811, 1; 31035996941, 1; 5979236519649901, 1
31^65+1 = [2, 5; 41, 1; 131, 1; 521, 1; 17863, 1; 21821, 1; 197271101, 1; 42716694944587, 1
28^67-1 = [3, 3; 39629149774235919086803410436533512071, 1
28^67+1 = [29, 1; 1313661738407, 1; 308410564740709, 1
44^59-1 = [43, 1; 709, 1
44^59+1 = [3, 2; 5, 1; 1181, 1; 31153, 1; 673073, 1; 8848563979237361, 1; 26281449623277513529586747689, 1
47^58+1 = [2, 1; 5, 1; 13, 1; 17, 1; 349, 1; 35729, 1; 2098441, 1
54^56+1 = [17, 1; 113, 1; 14593, 1; 291444977, 1; 181196478954035444944590621654811625681, 1
39^61-1 = [2, 1; 19, 1; 3539, 1; 1144483, 1; 9494708317, 1; 8779416156809261, 1
39^61+1 = [2, 3; 5, 1; 977, 1
33^64+1 = [2, 1; 3329, 1; 1404289, 1; 34232321, 1; 139982089033217, 1
19^76+1 = [2, 1; 17, 1; 3833, 1; 148490556214993, 1; 67552947210940643628327889, 1
17^79-1 = [2, 4; 2371, 1; 8849, 1; 32233, 1; 95294351981, 1
17^79+1 = [2, 1; 3, 2; 35485537, 1; 11672515136483, 1; 763172545882169, 1; 4431365126857943, 1; 2617152229311584271947, 1
37^62+1 = [2, 1; 5, 1; 137, 1; 4217, 1; 8733941, 1
35^63-1 = [2, 1; 13, 1; 17, 1; 19, 1; 43, 1; 97, 1; 127, 1; 3843127, 1; 44007727, 1; 96753079, 1; 50271355983367, 1; 3282747916283682841, 1
35^63+1 = [2, 2; 3, 4; 29, 1; 397, 1; 631, 1; 5209, 1; 6301, 1; 11831, 1; 612740917, 1; 3475688599752347161, 1
51^57-1 = [2, 1; 5, 2; 7, 1; 229, 1; 379, 1; 2357, 1; 1431119, 1; 23785887581, 1; 69264172403, 1
51^57+1 = [2, 2; 13, 1; 2053, 1; 2551, 1; 30553, 1; 40357, 1; 754022364308383, 1; 85189720388220845265139, 1
42^60+1 = [17, 1; 1201, 1; 183041, 1; 2651041, 1; 51536026081, 1; 9682648884721, 1; 1819187987193361, 1
14^85-1 = [11, 1; 13, 1; 103, 1; 1021, 1; 3761, 1; 5135191, 1; 22771730193675277, 1; 2045945611942276639291, 1
14^85+1 = [3, 1; 5, 2; 71, 1; 101, 1; 137, 1; 68171, 1; 498271, 1; 705161, 1; 22995901, 1; 329373710464831, 1; 14837638311110071, 1; 69901022666276891, 1
55^56+1 = [2, 1; 113, 1; 5203937, 1; 8045249, 1
30^66+1 = [17, 1; 53, 1; 9241, 1; 22441, 1; 34981, 1; 809101, 1; 5213693, 1; 7642669, 1; 66803214075022052730257, 1
48^58+1 = [5, 1; 461, 1; 7541, 1; 11717, 1; 55681, 1; 11356517, 1; 6183985351233699601, 1
45^59-1 = [2, 2; 11, 1; 31271, 1; 277301, 1; 950432036620886988739, 1
45^59+1 = [2, 1; 23, 1; 709, 1; 287921, 1; 2018981, 1; 39507581, 1; 135339943242693481811787472491293563, 1
20^75-1 = [11, 1; 19, 1; 31, 1; 61, 1; 151, 1; 251, 1; 421, 1; 1451, 1; 3001, 1; 11251, 1; 261451, 1; 1369801, 1; 7466201, 1; 46794901, 1; 9308203137060768572251, 1
20^75+1 = [3, 2; 7, 1; 101, 1; 127, 1; 152381, 1; 26876632021, 1; 51051875401, 1; 4273193518996201, 1; 1038193734970398415809901, 1
15^83-1 = [2, 1; 7, 1; 2158116330311, 1; 3220419108264156535849497113, 1
15^83+1 = [2, 4; 167, 1; 1163, 1; 3981350970411868479901, 1; 106776979377071844077873, 1
26^69-1 = [5, 2; 19, 1; 37, 1; 13709, 1; 1086199, 1; 1528507873, 1; 615551139461, 1
26^69+1 = [3, 4; 7, 1; 31, 1; 47, 1; 139, 1; 1157729, 1; 378673381, 1; 10706943763, 1; 629584013567417, 1
40^61-1 = [3, 1; 13, 1; 2441, 1; 21839, 1; 298584631, 1
40^61+1 = [41, 1; 367, 1; 733, 1; 65881, 1; 210838639830971, 1; 17577309021102349201386018089, 1
52^57-1 = [3, 2; 17, 1; 191, 1; 919, 1; 30211, 1; 30553, 1; 6997891, 1; 46723661, 1; 137961871813, 1; 126169954911757, 1
52^57+1 = [7, 1; 53, 1; 379, 1; 14783, 1; 512891005013876641620677411, 1
21^74+1 = [2, 1; 13, 1; 17, 1; 149, 1; 593, 1
56^56+1 = [17, 1; 11409217, 1; 5260913953, 1; 5689253622001, 1; 116868098415713, 1; 61716026883140982017, 1
18^78+1 = [5, 2; 13, 2; 53, 1; 157, 1; 229, 1; 313, 1; 457, 1; 21997, 1; 5210864257, 1; 5601346141, 1; 15715445027621, 1; 581721119015050561, 1
38^62+1 = [5, 1; 17, 2
29^67-1 = [2, 2; 7, 1; 4691, 1; 7237, 1
29^67+1 = [2, 1; 3, 1; 5, 1; 14741, 1; 173297930629746886212468111614816863, 1
24^71-1 = [23, 1
24^71+1 = [5, 2; 71569, 1; 39293109082181, 1; 57009162013493, 1; 48375351973455191295830483416567, 1
22^73-1 = [3, 1; 7, 1; 293, 1; 1585760683434492728054623403870583591611, 1
22^73+1 = [23, 1; 19293908309235221, 1; 4493831621328706884161237, 1; 4362374326112940284635767011, 1
43^60+1 = [2, 1; 17, 1; 73, 1; 97, 1; 193, 1; 313, 1; 521, 1; 25321, 1; 5273617, 1; 70937201, 1; 463847201, 1; 4151893201, 1; 633573428881, 1; 58781008890632761, 1
34^64+1 = [7477121, 1; 207413006868032513, 1; 1016641647219995495371861784486017, 1
13^88+1 = [2, 1; 4049, 1; 407865361, 1; 479397861182521358407441, 1; 1358999792679530608571000081, 1
23^72+1 = [2, 1; 17, 1; 3697, 1; 623009, 1; 1247329, 1; 12682129, 1; 454068345889, 1; 483563163219889, 1
46^59-1 = [3, 2; 5, 1; 130981, 1; 564930745883083815362557, 1
46^59+1 = [47, 1
53^57-1 = [2, 2; 7, 1; 13, 1; 229, 1; 409, 1; 11173, 1; 32688470798197, 1; 1482545708952391, 1; 1559280737801263, 1
53^57+1 = [2, 1; 3, 4; 919, 1; 822131, 1; 1423389637, 1; 1858193028673, 1; 9132358221258011, 1
41^61-1 = [2, 3; 5, 1; 4846906894369035343510985818467094997241059, 1
41^61+1 = [2, 1; 3, 1; 7, 1; 213623, 1; 679297, 1; 80823245238011, 1; 18138980389253695381, 1; 52977539531681055373519, 1
28^68+1 = [108529, 1; 302329, 1; 614657, 1; 809119897, 1; 5407933749161794928137748158777, 1
31^66+1 = [2, 1; 13, 1; 37, 1; 2729, 1; 922561, 1; 599382278617, 1; 169301958609793153, 1; 245911396799577828131028569, 1
17^80+1 = [2, 1; 257, 1; 3361, 1; 1801601, 1; 2033441, 1; 52548582913, 1
19^77-1 = [2, 1; 3, 2; 701, 1; 70841, 1; 73613, 1; 104281, 1; 62060021, 1
19^77+1 = [2, 2; 5, 1; 23, 1; 197, 1; 6469, 1; 226871, 1; 685034813, 1; 8090490101, 1; 253239693257, 1; 226288993450958131, 1
50^58+1 = [41, 1; 61, 1; 233, 1; 3727745029, 1; 121870914292722074399019296227780168709, 1
14^86+1 = [197, 1
44^60+1 = [41, 1; 113, 1; 641, 1; 809, 1; 11161, 1; 67801, 1; 239441, 1; 1699209601, 1; 14048219877121, 1; 59456780552203889508601, 1
39^62+1 = [2, 1; 761, 1; 4740931025208063757, 1
47^59-1 = [2, 1; 23, 1; 4603, 1; 256651, 1; 1234125153011903, 1; 32990983717854977, 1
47^59+1 = [2, 4; 3, 1; 709, 1; 827, 1; 8568354271357992900601687308271230418637, 1
33^65-1 = [2, 5; 31, 1; 131, 1; 39451, 1; 5586803, 1; 307870362047, 1; 825443633951, 1; 912556646431, 1
33^65+1 = [2, 1; 17, 1; 79, 1; 313, 1; 19709, 1; 571741, 1; 1151041, 1; 3321744947, 1; 3795466351, 1
54^57-1 = [53, 1; 457, 1; 2971, 1; 24311855176559, 1; 1397884427780837, 1
54^57+1 = [5, 1; 7, 1; 11, 1; 409, 1; 757417, 1; 2595530911, 1; 25087002870289750231, 1; 4798787200830201829483705663, 1
15^84+1 = [2, 1; 17, 1; 1489, 1; 10123513, 1; 2562840001, 1; 725177029417, 1; 766028506097, 1; 21975395880100433, 1
37^63-1 = [2, 2; 3, 4; 7, 2; 67, 1; 71, 1; 73, 1; 127, 1; 379, 1; 25453, 1; 92251, 1; 4497991, 1; 7992349, 1; 37140797, 1
37^63+1 = [2, 1; 19, 1; 31, 1; 43, 1; 199, 1; 631, 1; 12892843, 1; 1655684479, 1; 2498207293, 1; 4083348151, 1; 18449627617, 1; 25538742433, 1; 303340612177, 1
35^64+1 = [2, 1
20^76+1 = [457, 1; 160001, 1
30^67-1 = [29, 1; 5897, 1; 104921197, 1; 26401568180223414517611257, 1
30^67+1 = [31, 1; 269, 1; 2090184529, 1; 10928988277, 1; 10246155837002088910369, 1; 248498502835922332676119, 1
42^61-1 = [41, 1; 853814767889, 1; 3011347243007, 1; 380374960373003, 1; 81759426276425182777, 1
42^61+1 = [43, 1; 17863283569307161736407, 1
51^58+1 = [2, 1; 1301, 1; 15313, 1; 147474375701, 1
26^70+1 = [29, 1; 677, 1; 4733, 1; 208518605101, 1; 694230517093, 1
13^89-1 = [2, 2; 3, 1; 179, 1; 9257, 1; 716164560927079240026189379811, 1
13^89+1 = [2, 1; 7, 1; 21001153, 1; 2197020880176009487, 1; 410771620528283009753757952793, 1
21^75-1 = [2, 2; 5, 3; 151, 1; 211, 1; 463, 1; 1051, 1; 1801, 1; 9391, 1; 18181, 1; 40841, 1; 2031851, 1; 9728219701, 1; 201307465501, 1; 27385718497004633851, 1
21^75+1 = [2, 1; 11, 1; 31, 1; 101, 1; 421, 1; 2551, 1; 185641, 1; 386851, 1; 501001, 1; 11093851, 1; 263977951, 1; 895322420811001, 1; 248303068144516751, 1
18^79-1 = [17, 1; 338279, 1; 1104737, 1; 12802037494726063, 1; 9886837665707422272737, 1
18^79+1 = [19, 1; 1735973262881810486884626006469367486329, 1
45^60+1 = [2, 1; 241, 1; 401, 1; 2161, 1; 5113, 1; 35569, 1; 472746529, 1; 6871250180401, 1; 130841449768595473867441, 1
48^59-1 = [47, 1; 52511, 1; 2265887836608864040905434730500399, 1
48^59+1 = [7, 2; 7789, 1; 369724681, 1; 947530325982934315368121, 1
55^57-1 = [2, 1; 3, 4; 13, 1; 79, 1; 229, 1; 571, 1; 647, 1; 1483, 1; 1397983, 1; 18145951, 1; 7015010443435663, 1; 3222383446162535363, 1
55^57+1 = [2, 3; 7, 1; 191, 1; 2971, 1; 14783, 1; 535991, 1; 13764157447830986477, 1; 124724246202276843883, 1
40^62+1 = [1601, 1; 27281, 1; 29683741, 1; 9934573793351813543760747276183581, 1
22^74+1 = [5, 1; 97, 1; 105196921, 1; 1322219481421, 1
24^72+1 = [17, 1; 2801, 1; 33409, 1; 2311681, 1; 13308961, 1; 27250359649, 1
23^73-1 = [2, 1; 11, 1; 632911, 1; 3467983074289, 1
23^73+1 = [2, 3; 3, 1; 82897487, 1; 33634861877050507067251, 1; 195436881937205119535750400397, 1
29^68+1 = [2, 1; 137, 1; 132329, 1; 353641, 1; 541195001, 1; 1680586273, 1; 69424250262848801, 1; 10774466250435548293033, 1
38^63-1 = [37, 1; 43, 1; 109, 1; 127, 2; 163, 1; 1483, 1; 39439, 1; 136963, 1; 169471, 1; 92928739, 1; 3092313043, 1; 635444013053181403, 1
38^63+1 = [3, 3; 7, 2; 13, 1; 29, 1; 67, 1; 211, 1; 239, 1; 423277, 1; 1003627171, 1; 4481119419463, 1; 6299350303205107, 1
52^58+1 = [5, 1; 233, 1; 349, 1; 541, 1; 5801, 1; 42689, 1; 31781442789179720313978785299510141, 1
34^65-1 = [3, 1; 11, 1; 61, 1; 131, 1; 2341, 1; 12611, 1; 22571, 1; 498802573647613561, 1; 2458736461986831391, 1
34^65+1 = [5, 2; 7, 1; 16381, 1; 259631, 1; 2009983, 1; 13303573531, 1; 1153361613301, 1
43^61-1 = [2, 1; 3, 1; 7, 1; 8663, 1; 1040227478461885061399, 1
43^61+1 = [2, 2; 11, 1; 375028741517, 1
56^57-1 = [5, 1; 11, 1; 31, 1; 103, 1; 647, 2; 108304561, 1; 3615436547, 1; 5224985521849, 1; 19735153944503363, 1
56^57+1 = [3, 2; 13, 1; 19, 2; 79, 1; 229, 1; 4637, 1; 16987, 1; 3791033, 1; 14766877, 1; 86287799881092363079, 1
17^81-1 = [2, 4; 19, 1; 307, 1; 433, 1; 24733, 1; 1270657, 1; 6770748529, 1; 454194717025663, 1; 1313154695584063, 1
17^81+1 = [2, 1; 3, 6; 7, 1; 13, 1; 163, 1; 811, 1; 1423, 1; 2269, 1; 5653, 1; 1792803781, 1; 78044489325524647, 1; 28758863909916435817, 1
14^87-1 = [13, 1; 211, 1; 349, 1; 13109, 1; 100577221, 1; 25581350023, 1; 396530555859061913, 1
14^87+1 = [3, 2; 5, 1; 59, 1; 61, 1; 523, 1; 7345482559, 1; 114221024581, 1; 17101086842968403641, 1; 1588794541523975089627189, 1
19^78+1 = [2, 1; 13, 3; 53, 1; 181, 1; 769, 1; 92174159182574048847888178637, 1
46^60+1 = [4477457, 1; 20047607754481, 1; 401906666439788301510827761, 1
28^69-1 = [3, 4; 47, 1; 139, 1; 271, 1; 277, 1; 224727078564911869, 1; 1517655145813456319033978812579, 1
28^69+1 = [29, 1; 757, 1; 7039, 1; 94369507, 1; 115152031, 1; 140668620541, 1; 255595103341, 1; 4099849287367, 1
31^67-1 = [2, 1; 3, 1; 5, 1; 882659, 1; 447772934301264047325373, 1; 1334574386438395108609084044317, 1
31^67+1 = [2, 5; 561825821, 1; 434585936689, 1; 215725957975181, 1; 111558400193618429, 1; 1718795629713735456383, 1
15^85-1 = [2, 1; 7, 1; 11, 1; 4931, 1; 1045002649, 1; 6734509609, 1
15^85+1 = [2, 4; 31, 1; 137, 1; 443, 1; 1531, 1; 2551, 1; 13695697627231, 1; 101462866544971, 1
41^62+1 = [2, 1; 29, 2; 19254211601, 1; 12175812483469, 1
53^58+1 = [2, 1; 5, 1; 281, 1; 349, 1; 1277, 1; 13109, 1; 44893, 1
57^57-1 = [2, 3; 7, 1; 229, 1; 3307, 1; 208963, 1; 858083110267312575697141, 1; 14710826638296122001733445931451, 1
57^57+1 = [2, 1; 29, 1; 31, 1; 103, 1; 4561, 1; 8209, 1; 9349, 1; 62207, 1; 22611179, 1; 16453188397, 1; 3433535507453509, 1; 21270230934999421, 1
20^77-1 = [19, 1; 29, 1; 71, 1; 32719, 1; 10778947368421, 1; 11591111347512862858060061, 1
20^77+1 = [3, 1; 7, 2; 23, 1; 827, 1; 10529, 1; 424016563147, 1
33^66+1 = [2, 1; 5, 1; 13, 1; 109, 1; 7129, 1; 91141, 1; 125929, 1; 3920401, 1; 18610345022908326918950809, 1
39^63-1 = [2, 1; 7, 2; 19, 1; 181, 1; 223, 1; 379, 1; 2857, 1; 606733, 1; 1264033, 1; 19440901, 1; 72796627, 1; 7494915289, 1; 46203580155727, 1
39^63+1 = [2, 3; 5, 1; 43, 1; 71, 1; 127, 1; 547, 1; 1483, 1; 2089, 1; 727063, 1; 1123739, 1; 1684387, 1; 31930371901, 1
50^59-1 = [7, 2; 2050487, 1; 5299521247, 1; 11220403906414151, 1
50^59+1 = [3, 1; 17, 1; 14195873, 1; 44523643, 1; 50966213714723, 1
44^61-1 = [43, 1; 384694061, 1; 275843501360449314073499968475209143446929, 1
44^61+1 = [3, 2; 5, 1; 367, 1; 4271, 1; 41603, 1; 81250639105739, 1; 131970140524635594157, 1; 53012781617970566757908717, 1
13^90+1 = [2, 1; 5, 2; 17, 1; 37, 1; 421, 1; 601, 1; 641, 1; 28393, 1; 428041, 1; 1471069, 1; 460655521, 1; 1453046401, 1; 14513462249341141, 1
47^60+1 = [2, 1; 41, 1; 97, 1; 241, 1; 25153, 1; 592121, 1; 3781801, 1; 6296281, 1; 1650281815098481, 1; 96906804901341361, 1
35^65-1 = [2, 1; 17, 1; 31, 1; 131, 1; 443, 1; 49831, 1; 7852391301419627, 1
35^65+1 = [2, 2; 3, 2; 11, 1; 132631, 1; 373361, 1; 3285353271721733941, 1
37^64+1 = [2, 1; 1212165617153, 1
18^80+1 = [3930785153, 1; 17619087361, 1; 30894471809, 1; 545145333573761, 1
30^68+1 = [241, 1; 3361, 1; 3673, 1; 141264028412449, 1
26^71-1 = [5, 2; 1475239, 1; 2270440490478175159386113, 1; 440314247117511584166211925609, 1
26^71+1 = [3, 3; 569, 1; 297063007, 1
54^58+1 = [2917, 1; 6961, 1; 33354757, 1; 69394333, 1; 3918911156341, 1
21^76+1 = [2, 1; 97241, 1; 136649, 1; 6629177, 1; 8871582886760161, 1; 4370570172021545617284038736601, 1
42^62+1 = [5, 1; 353, 1; 27653, 1; 4947196423396642966182984831168841, 1
22^75-1 = [3, 2; 7, 1; 13, 2; 61, 1; 151, 1; 245411, 1; 452701, 1; 210499351, 1; 858794191, 1; 503676620401, 1; 6474393278401, 1; 10605157372501, 1
22^75+1 = [23, 1; 31, 1; 101, 1; 463, 1; 154001, 1; 224071, 1; 727351, 1; 821101, 1; 1850478481, 1; 12338584051, 1; 62354037124651, 1
51^59-1 = [2, 1; 5, 2; 34932839, 1; 25752385727, 1
51^59+1 = [2, 2; 13, 1; 827, 1; 3863911, 1; 6913604326255227223695717362894743327, 1
24^73-1 = [23, 1; 293, 1; 3359, 1; 70373, 1; 478589, 1
24^73+1 = [5, 2; 439, 1; 1034657962731961050103352235001, 1
23^74+1 = [2, 1; 5, 1; 53, 1; 149, 1; 571873, 1; 65887757401, 1
45^61-1 = [2, 2; 11, 1; 4759, 1; 27329, 1; 3410630737301, 1; 14390821700656021, 1
45^61+1 = [2, 1; 23, 1; 367, 1; 12689, 1; 8003201, 1; 19180018758221, 1; 214553033898100484087, 1
14^88+1 = [17, 1; 5393, 1; 16097, 1; 726776513, 1; 27839910162900081267786564789267761898449, 1
48^60+1 = [41, 1; 241, 1; 1721, 1; 2161, 1; 8929, 1; 1140721, 1; 5308417, 1; 9187201, 1; 3155927329, 1; 13427893441, 1; 18942781201, 1; 212536121402641, 1
17^82+1 = [2, 1; 5, 1; 29, 1; 10954332408956399140877, 1
29^69-1 = [2, 2; 7, 1; 13, 1; 67, 1; 139, 1; 131327761273, 1; 1173922372300235340427, 1
29^69+1 = [2, 1; 3, 2; 5, 1; 47, 1; 271, 1; 277, 1; 12697, 1; 32983, 1; 7637473, 1; 47204232433066302943, 1; 548044326578988272558591797, 1
40^63-1 = [3, 3; 13, 1; 43, 1; 163, 1; 547, 1; 631, 1; 8317, 1; 9199, 1; 7879999, 1; 8376409, 1; 4201025641, 1
40^63+1 = [7, 2; 19, 1; 37, 1; 41, 1; 127, 1; 211, 1; 223, 1; 379, 1; 1009, 1; 6007, 1; 15373, 1; 18938851, 1; 3220160975767, 1; 957723887056210659504251623, 1
55^58+1 = [2, 1; 17, 1; 89, 1; 233, 1; 18097, 1; 123462741184333, 1; 5264367611260711303829, 1
19^79-1 = [2, 1; 3, 2; 10429, 1; 32233, 1; 1380763, 1
19^79+1 = [2, 2; 5, 1; 25871039291, 1
34^66+1 = [13, 1; 89, 1; 353, 1; 1069, 1; 1249, 1; 15797, 1; 50777, 1; 15037874431339441793, 1; 180671731958047148281, 1
38^64+1 = [769, 1; 1153, 1; 4617960833, 1
15^86+1 = [2, 1; 113, 1; 20641, 1; 3187525094785565082363106129, 1
52^59-1 = [3, 1; 17, 1; 24557857971331, 1; 3641125927249697, 1; 29170813553478370523947569707, 1
52^59+1 = [53, 1; 71596616199793, 1; 899726268990495517, 1
43^62+1 = [2, 1; 5, 2; 37, 1; 12401, 1
28^70+1 = [5, 2; 61, 1; 157, 1; 281, 1; 14561, 1; 84961, 1; 749729, 1; 924841, 1; 25917641, 1; 1100860153, 1
13^91-1 = [2, 2; 3, 1; 53, 1; 10193, 1; 34763, 1; 264031, 1; 1326781, 1; 1803647, 1; 5229043, 1; 72019220497491955875703699, 1
13^91+1 = [2, 1; 7, 2; 29, 1; 4733, 1; 13417, 1; 20333, 1; 22079, 1; 79301, 1; 6176383648709, 1; 244409090738941856729, 1
56^58+1 = [233, 1; 3137, 1; 75401, 1; 318063070079696257, 1; 70780928379551596652386671329, 1
31^68+1 = [2, 1; 137, 1; 409, 1; 953, 1; 1129, 1; 11833, 1; 63574561, 1
46^61-1 = [3, 2; 5, 1; 367, 1; 3360847507788056693645113, 1
46^61+1 = [47, 1; 3539, 1; 155992007, 1; 18683396789960768890997894543901691, 1
20^78+1 = [13, 2; 53, 1; 157, 1; 401, 1; 12277, 1; 502321, 1; 670533425797, 1; 106896982629956973639277, 1; 628605693732325702045277, 1
41^63-1 = [2, 3; 5, 1; 43, 1; 127, 1; 379, 1; 487, 1; 631, 1; 1723, 1; 4159, 1; 8339563, 1; 9753949, 1; 113229229, 1; 633071522245681, 1; 22013480670406449841, 1
41^63+1 = [2, 1; 3, 3; 7, 2; 19, 1; 37, 1; 71, 1; 73, 1; 547, 1; 30853, 1; 604801, 1; 9329993, 1; 532231354645142167, 1; 23113483969970021041, 1
18^81-1 = [7, 3; 17, 1; 487, 1; 991, 1; 23761, 1; 34327, 1; 253369, 1; 1464049, 1; 4464073, 1; 27470503, 1; 1964508729666289645801020967, 1
18^81+1 = [19, 1; 73, 1; 163, 1; 307, 1; 465841, 1; 108813457, 1; 3211621489, 1; 31865908033, 1; 1234749313729, 1; 2822726926367077537, 1
53^59-1 = [2, 2; 13, 1; 943970114867362247759443, 1; 12466526280783961115381107, 1
53^59+1 = [2, 1; 3, 3; 36109, 1; 9297103, 1; 3800202410345894347927417, 1; 21885671994461001493726693163797, 1
33^67-1 = [2, 5; 4289, 1; 1084112663, 1; 11098897650130502135455967441, 1; 18560847411975948968564462623, 1
33^67+1 = [2, 1; 17, 1
21^77-1 = [2, 2; 5, 1; 43, 1; 631, 1; 3319, 1; 6225803431, 1; 17513875027111, 1; 39824892937303186001525100993399811, 1
21^77+1 = [2, 1; 11, 2; 23, 1; 6073, 1; 10362529, 1; 81867661, 1; 123679698913, 1; 15502260840362954719909, 1; 37681894326794146626121, 1
39^64+1 = [2, 1; 501015937, 1
57^58+1 = [2, 1; 5, 3; 13, 1; 20533, 1; 38629, 1; 142317474992103577, 1; 43180312279690250582407169, 1
26^72+1 = [3617, 1; 57734881, 1; 25662210913, 1; 1699336937377, 1; 2303220087073, 1; 9849511001030257, 1
44^62+1 = [13, 1; 149, 1; 8751214858349487946085643199510773255089, 1
35^66+1 = [2, 1; 277, 1; 353, 1; 613, 1; 5413, 1; 60457, 1; 3981209, 1; 6913457, 1; 12944192537, 1; 2964674178069172537, 1
30^69-1 = [7, 2; 19, 1; 29, 1; 139, 1; 277, 1; 461, 1; 691, 1; 2716117, 1; 148927117, 1; 1733583601, 1; 9846720119, 1; 1377813914401, 1; 6785569740223, 1
30^69+1 = [13, 1; 31, 1; 47, 1; 67, 1; 1933, 1; 89541163, 1; 148414723, 1; 1982852173, 1; 21956442933767, 1; 14380755448480627, 1; 34140313913055733, 1
37^65-1 = [2, 2; 3, 2; 11, 1; 41, 1; 4271, 1; 6765811783780036261, 1; 2153555189014162710765708277712188711, 1
37^65+1 = [2, 1; 19, 1; 53, 1; 131, 1; 521, 1; 2341, 1; 591163, 1; 1824841, 1; 26668430231, 1; 204576480239, 1; 4230861918113529109820495971, 1
50^60+1 = [97, 1; 241, 1; 4801, 1; 64433, 1; 1874881, 1; 617094241, 1; 39062493750001, 1; 2472683361356169361, 1
47^61-1 = [2, 1; 23, 1; 367, 1; 5951132410461230489781053801575957985375412445883, 1
47^61+1 = [2, 4; 3, 1; 733, 1; 82505918259333162378991, 1; 72130802342268278028043776613, 1
14^89-1 = [13, 1; 179, 1; 3264343, 1; 72284972657, 1; 558880233911, 1
14^89+1 = [3, 1; 5, 1; 1485227518551701761601, 1
22^76+1 = [73, 1; 457, 1; 3209, 1; 2999569, 1; 34356713, 1; 381921737, 1; 75009303521, 1; 471300292422508768026225597793, 1
17^83-1 = [2, 4; 186917, 1; 1441585450365875501, 1; 859764623611313847689900219, 1
17^83+1 = [2, 1; 3, 2; 167, 1; 28387, 1; 974813135809, 1
23^75-1 = [2, 1; 7, 1; 11, 1; 79, 1; 6551, 1; 292561, 1; 74912328481, 1; 2700470569501, 1; 261968569374120475321751, 1
23^75+1 = [2, 3; 3, 2; 13, 2; 31, 1; 41, 1; 101, 1; 151, 1; 211, 1; 56951, 1; 1068701, 1; 5635501, 1; 541119751, 1; 279175761283651, 1
24^74+1 = [577, 1; 62039080369751004680569, 1
54^59-1 = [53, 1; 4013, 1; 105786647, 1; 3107096944460816323298986967, 1
54^59+1 = [5, 1; 11, 1; 207439587020189, 1; 391600580957541681107, 1; 3173348287333655783884840344347, 1
42^63-1 = [13, 1; 19, 1; 41, 1; 127, 1; 139, 1; 1009, 1; 3851, 1; 1460117, 1; 7124839, 1; 25516009, 1; 288900307, 1; 4091341129, 1; 1985468030407, 1
42^63+1 = [29, 1; 43, 1; 337, 1; 547, 1; 1723, 1; 19489, 1; 548591, 1; 5488957657, 1; 1579727718577, 1; 2893529445073, 1
58^58+1 = [5, 1; 349, 1; 673, 1; 929, 1; 4177, 1; 24709, 1; 59393, 1; 87697, 1; 607458013, 1; 2432306677, 1; 55525285001, 1; 1309401006591358303313, 1
19^80+1 = [2, 1; 97, 1; 5441, 1; 113921, 1; 1486811410142377153, 1; 6163870442158237952544812259041, 1
15^87-1 = [2, 1; 7, 1; 59, 1; 241, 1; 349, 1; 798084409, 1; 15476275967141572773889537007699, 1
15^87+1 = [2, 4; 211, 1; 1831362215404162343599, 1; 798962746803683694452047348022461, 1
29^70+1 = [2, 1; 421, 1; 1061, 1; 427822081, 1; 470925821, 1; 826031641, 1; 59696006212089310421, 1
51^60+1 = [2, 1; 73, 1; 38921, 1; 46337, 1; 56737, 1; 506201, 1; 806668273, 1; 1217517841, 1; 1350336443816641, 1; 106320195008359681, 1
13^92+1 = [2, 1; 1657, 1; 14281, 1; 10093085551851597657003882281641, 1; 13083857523758118007762301611817, 1
45^62+1 = [2, 1; 373, 1; 1013, 1; 1117, 1; 1863991276087044361, 1; 1173092525145410298163600487053, 1
40^64+1 = [438913, 1; 72209449209995137, 1; 275265972634797415553, 1; 36456537995564380745801814913, 1
48^61-1 = [47, 1; 6295979327493762037, 1; 3318484479336240782385604991, 1
48^61+1 = [7, 2; 20415847, 1; 12494240785597, 1; 125857943168739619, 1
34^67-1 = [3, 1; 11, 1; 915506774873063, 1
34^67+1 = [5, 1; 7, 1; 269, 1; 381097, 1; 930229, 1; 57424093, 1
55^59-1 = [2, 1; 3, 3; 7848924574476367455250910280066079643, 1
55^59+1 = [2, 3; 7, 1; 5512462129845673, 1
38^65-1 = [11, 1; 37, 1; 79, 1; 131, 1; 443, 1; 194681, 1; 48594521, 1; 77816243441, 1; 262751819201, 1; 266044456723943, 1
38^65+1 = [3, 1; 13, 2; 53, 1; 547, 1; 368369, 1; 2031671, 1; 63625693, 1; 133464055195154910688541, 1
28^71-1 = [3, 3; 25828494169, 1; 37313251966817, 1; 857600610882384989993501, 1
28^71+1 = [29, 1; 2651845457, 1; 4252745790841, 1
20^79-1 = [19, 1; 26861, 1; 7731160503875069, 1; 4178614725165165091, 1; 52283868973702536169, 1
20^79+1 = [3, 1; 7, 1
31^69-1 = [2, 1; 3, 2; 5, 1; 139, 1; 331, 1; 1164859, 1; 1509997, 1; 61562537, 1; 2553526979752336381, 1; 7176374761323733117, 1
31^69+1 = [2, 5; 7, 2; 19, 1; 47, 1; 6073, 1; 117071611, 1; 45414448613, 1; 293006379555093281221, 1
43^63-1 = [2, 1; 3, 3; 7, 2; 19, 1; 181, 1; 199, 1; 211, 1; 631, 1; 3079, 1; 5839, 1; 158341, 1; 84110461, 1; 2199253519, 1; 13188379540771, 1
43^63+1 = [2, 2; 11, 1; 13, 1; 109, 1; 127, 1; 139, 1; 4831, 1; 57993427, 1; 65299879, 1; 6177695707, 1; 66222479233, 1; 390939633981037, 1; 8463757040413879, 1
18^82+1 = [5, 2; 13, 1; 117012619172903468336363755054149226979817746816041, 1
52^60+1 = [41, 1; 73, 1; 89, 1; 12401, 1; 24793, 1; 82153, 1; 29537569, 1; 7727786401, 1; 727373986441, 1; 92518384980297951001, 1
46^62+1 = [29, 1; 73, 1; 1117, 1; 1416131680122073, 1; 2670225170657399737, 1; 13231191726896104407149177, 1
21^78+1 = [2, 1; 13, 2; 17, 1; 53, 1; 61, 1; 157, 1; 3181, 1; 6709, 1; 32969, 1; 101089, 1; 23509884574335185209, 1; 193538987428465501811153413, 1
56^59-1 = [5, 1; 11, 1; 262079, 1; 827309683, 1; 382384535971, 1
56^59+1 = [3, 1; 19, 1; 264139083883261, 1; 11597816857937357, 1; 100138343014110581, 1
14^90+1 = [37, 1; 197, 1; 1033, 1; 1061, 1; 1383881, 1; 56693904845761, 1; 2189065053896955781, 1; 45555678436399855012801, 1
41^64+1 = [2, 1; 120577, 1; 93040814849, 1; 80350880823867160961, 1; 326549946497470306390924033, 1
33^68+1 = [2, 1; 97, 1; 137, 1; 6113, 1; 20809, 1; 2430316601, 1; 21373531350655016111130353, 1
26^73-1 = [5, 2; 293, 1; 1574553353, 1
26^73+1 = [3, 3; 877, 1; 3067, 1; 71302486471, 1; 3015022137777309849949579, 1
17^84+1 = [2, 1; 73, 1; 1321, 1; 2801, 1; 15121, 1; 41761, 1; 72337, 1; 12876020081, 1; 622434484561, 1; 788614047082016621761, 1
22^77-1 = [3, 1; 7, 2; 67, 1; 353, 1; 16968421, 1; 61303243, 1; 1176469537, 1; 6294765596659, 1
22^77+1 = [23, 1; 29, 1; 43, 1; 89, 1; 86969, 1; 285451051007, 1
30^70+1 = [17, 1; 53, 1; 54121, 1; 572573, 1; 12109381, 1; 460980075781, 1; 927132724337, 1
39^65-1 = [2, 1; 19, 1; 31, 1; 131, 1; 157, 1; 191, 1; 401, 1; 911, 1; 3251, 1; 19442203086541, 1; 617853265920983, 1
39^65+1 = [2, 3; 5, 2; 11, 1; 3511, 1; 41011, 1; 890150815065246151, 1; 12072018714187014493, 1; 818590775898418767898525561, 1
35^67-1 = [2, 1; 17, 1; 7907, 1
35^67+1 = [2, 2; 3, 2; 38459, 1
53^60+1 = [2, 1; 17, 1; 41, 1; 241, 1; 4201, 1; 232073, 1; 45110321, 1; 3915250681, 1; 62259682520881, 1; 2095820501519891401, 1
23^76+1 = [2, 1; 15809, 1; 139921, 1; 40308694338467297, 1
15^88+1 = [2, 1; 353, 1; 3697, 1; 7121, 1; 179953, 1; 62263707129997297, 1; 1285545509619454513, 1
37^66+1 = [2, 1; 5, 1; 13, 1; 137, 1; 1277, 1; 144061, 1; 716402017, 1; 11858150701, 1; 1525285299913, 1; 11862476916440261, 1; 1455882262151801749, 1
24^75-1 = [23, 1; 101, 1; 241, 1; 601, 1; 14401, 1; 17881, 1; 24481, 1; 33601, 1; 36451, 1; 44851, 1; 346201, 1; 1661037601, 1; 23962054482148301, 1
24^75+1 = [5, 4; 7, 1; 11, 1; 31, 1; 79, 1; 151, 1; 1201, 1; 3391, 1; 4801, 1; 5791, 1; 7951, 1; 21001, 1; 86501, 1; 1090681, 1; 46739551, 1; 165634351, 1; 18538334327856439351, 1
44^63-1 = [7, 2; 19, 1; 37, 1; 43, 1; 127, 1; 239, 1; 283, 1; 1163, 1; 3739, 1; 6679, 1; 26713, 1; 41077, 1; 10322047, 1; 1235512909, 1; 35972410313701, 1; 1966072325539897, 1
44^63+1 = [3, 4; 5, 1; 379, 1; 631, 1; 15139, 1; 55819, 1; 159769, 1; 7095062437, 1; 964727825565799, 1
19^81-1 = [2, 1; 3, 6; 127, 1; 487, 1; 523, 1; 3727, 1; 29989, 1; 216919, 1; 907471, 1; 362063089, 1
19^81+1 = [2, 2; 5, 1; 7, 3; 163, 1; 199, 1; 41203, 1; 236377, 1; 2522827, 1; 1001724990823, 1
57^59-1 = [2, 3; 7, 1; 1401639401, 1; 13228150343, 1; 315694938911709823, 1; 26530185059968803558860351, 1
57^59+1 = [2, 1; 29, 1; 2243, 1; 27967, 1; 427076792183, 1; 1596893930485278504731083498402051, 1
13^93-1 = [2, 2; 3, 2; 61, 1; 311, 1; 1117, 1; 1303, 1; 6377362657, 1; 109711631401199502223, 1; 8170509011431363408568150369, 1
13^93+1 = [2, 1; 7, 1; 157, 1; 373, 1; 2729, 1; 23623, 1; 145831193, 1; 16389023943543602257, 1
50^61-1 = [7, 2; 2441, 1; 1339016086140839, 1; 815287727075024814767183, 1
50^61+1 = [3, 1; 17, 1; 29792388289, 1
47^62+1 = [2, 1; 5, 1; 13, 1; 17, 1; 224824713024803026981562696519938343177, 1
29^71-1 = [2, 2; 7, 1; 31621513293496729, 1; 5885237414620874027, 1; 575922000923214999444714868141, 1
29^71+1 = [2, 1; 3, 1; 5, 1; 83448009153877893908450153, 1; 253551009241878644908108309, 1
42^64+1 = [257, 1; 641, 1; 4481, 1; 15233, 1; 720569345052631937, 1; 59532284236561896692702595847851521, 1
54^60+1 = [41, 1; 97, 1; 337, 1; 433, 1; 5108113, 1; 8503057, 1; 127501780456057632484138121, 1
58^59-1 = [3, 1; 19, 1; 9323, 1; 3986513, 1
58^59+1 = [59, 2; 394502321, 1; 214457733089, 1; 44831246727500282353, 1; 357679573320929012069237, 1
20^80+1 = [97, 1; 6756288659793814433, 1
40^65-1 = [3, 1; 13, 2; 677, 1; 6917, 1; 2625641, 1; 282660734773, 1; 3020999518681, 1
40^65+1 = [11, 2; 41, 1; 53, 1; 131, 1; 20641, 1; 85558721, 1; 3609573397, 1; 138203542361, 1; 14818584429611, 1; 50345419305822396211, 1
34^68+1 = [62017, 1; 1336337, 1
45^63-1 = [2, 2; 11, 1; 19, 1; 29, 1; 71, 1; 109, 1; 10009, 1; 829639, 1; 3561391, 1; 4124569, 1; 1624694359, 1; 23709916819, 1; 41497642159, 1
45^63+1 = [2, 1; 7, 2; 23, 1; 43, 1; 127, 1; 283, 1; 883, 1; 7309, 1; 274723, 1; 1136089, 1; 188912767, 1; 41508491767, 1; 1921676813029, 1; 7100197990996321, 1
51^61-1 = [2, 1; 5, 2; 495199, 1; 72001351, 1
51^61+1 = [2, 2; 13, 1; 11584894667, 1
18^83-1 = [17, 1; 167, 1; 59263, 1; 86802964875867109109279559751944809, 1
18^83+1 = [19, 1; 499, 1; 207833, 1; 531646634129969, 1
28^72+1 = [17, 1; 193, 1; 12241, 1; 59809, 1; 151201, 1; 33806737, 1; 365764369, 1; 1350615169, 1; 22223646961, 1
48^62+1 = [5, 1; 461, 1; 53693, 1; 7610326277, 1
38^66+1 = [5, 1; 17, 2; 2113, 1; 2083693, 1; 535100369, 1; 1063619833, 1; 73609866148901550291869, 1
14^91-1 = [13, 2; 157, 1; 8108731, 1; 29914249171, 1; 28814088661742931457, 1; 1831232267609932496997868363, 1
14^91+1 = [3, 1; 5, 1; 79, 1; 911, 1; 7307, 1; 100621, 1; 7027567, 1; 30241695871297, 1
31^70+1 = [2, 1; 13, 1; 29, 1; 37, 1; 181, 1; 281, 1; 7253, 1; 13469, 1; 106261, 1; 107941, 1; 277739477, 1; 4707206941, 1; 77890519715454496560396129461, 1
55^60+1 = [2, 1; 41, 1; 193, 1; 65929, 1; 111593, 1; 6580633, 1; 2871622801, 1; 68822222881, 1; 4485234541681, 1; 1563211806048721, 1
21^79-1 = [2, 2; 5, 1; 2687, 1; 10903, 1; 15208288358346544216626697, 1; 122435283552586211204658864416622901, 1
21^79+1 = [2, 1; 11, 1; 41784481746279594641483665441943191140798018660203, 1
59^59-1 = [2, 1; 29, 1; 709, 1; 141579233, 1
59^59+1 = [2, 2; 3, 1; 5, 1; 4466419, 1; 27759619, 1; 6806872605199, 1; 11821911653180627, 1; 114888627555970745944996436263, 1
43^64+1 = [2, 1; 178061441, 1; 827493655762177, 1
17^85-1 = [2, 4; 5441, 1; 10949, 1; 88741, 1; 208931, 1; 1749233, 1; 22296011, 1; 24543581, 1; 2699538733, 1; 4939937011021, 1; 7517339434046845421, 1
17^85+1 = [2, 1; 3, 2; 11, 1; 71, 1; 101, 1; 45957792327018709121, 1; 414560726212391729865517272853661, 1
15^89-1 = [2, 1; 7, 1; 179, 1; 807409, 1; 18500463452718361, 1
15^89+1 = [2, 4; 12684688516982941, 1
52^61-1 = [3, 1; 17, 1; 367, 1
52^61+1 = [53, 1; 14153, 1; 34649, 1; 763843, 1; 607074726701, 1; 181934475175546400737, 1
26^74+1 = [677, 1; 3701, 1; 1863913, 1; 643138001477, 1; 2614341098911181, 1; 378035719977018250810259472301, 1
22^78+1 = [5, 1; 53, 1; 97, 1; 157, 1; 313, 1; 1489, 1; 498733, 1; 673297, 1; 36365629, 1; 2468996151857, 1; 2526873929581, 1
13^94+1 = [2, 1; 5, 1; 17, 1; 36097, 1; 75389, 1; 99886248944632632917, 1
46^63-1 = [3, 4; 5, 1; 7, 2; 37, 1; 103, 1; 307, 1; 62497, 1; 278029, 1; 1174474099, 1; 9684836827, 1; 10680993247, 1; 16994062455360514407092917, 1
46^63+1 = [19, 1; 43, 1; 47, 1; 109, 1; 127, 1; 757, 1; 5581, 1; 139483, 1; 1697581, 1; 20945317, 1; 9272716111, 1; 101829626641, 1; 47629811054297760850171, 1
33^69-1 = [2, 5; 461, 1; 1123, 1; 3911, 1; 350026513, 1; 1461106583208387755192310613, 1
33^69+1 = [2, 1; 7, 1; 17, 1; 47, 1; 139, 1; 151, 1; 26681, 1; 488797, 1; 4551103, 1; 7390039, 1; 90503207, 1; 107880397, 1; 235399159, 1; 21267490133, 1; 477102479059, 1
41^65-1 = [2, 3; 5, 2; 131, 1; 1171, 1; 11831, 1; 110969, 1; 579281, 1; 17615988547, 1
41^65+1 = [2, 1; 3, 1; 7, 1; 11, 1; 61, 1; 79, 1; 4111, 1; 432589, 1; 644522798011, 1; 9335596834981, 1; 33574965983093338194578727584591, 1
23^77-1 = [2, 1; 11, 2; 29, 1; 5336717, 1; 3937230404603, 1; 182688705194696220829, 1
23^77+1 = [2, 3; 3, 1; 71, 1; 463, 1; 673, 1; 2969, 1; 9980279, 1; 3471747294401, 1; 39700406579747, 1; 604282871748410869340577637, 1
19^82+1 = [2, 1; 181, 1; 8693, 1; 429905758180413633468024775816828725077, 1
30^71-1 = [29, 1; 2557, 1; 55640287, 1; 7357260409416410663267, 1
30^71+1 = [31, 1; 19597, 1; 18380339, 1; 6914384231924331500092352689697439862798457, 1
56^60+1 = [41, 1; 73, 1; 100801, 1; 9834497, 1; 1324894544377, 1; 16808541046614054121, 1; 228152131876570054227659801, 1
24^76+1 = [99257, 1; 331777, 1
35^68+1 = [2, 1; 137, 1; 2857, 1; 7481, 1; 20129, 1; 750313, 1; 5576852993, 1
39^66+1 = [2, 1; 761, 1; 3433, 1; 22573, 1; 1671121, 1; 2311921, 1; 260592377, 1; 5387785552117, 1; 74023768574167426961, 1
37^67-1 = [2, 2; 3, 2; 269, 1; 446221, 1; 152396765001287591, 1
37^67+1 = [2, 1; 19, 1; 31153274141213881, 1
53^61-1 = [2, 2; 13, 1; 4852617050313249081293371405555776730569547, 1
53^61+1 = [2, 1; 3, 3; 8194778217125403181132925846320901250851405699, 1
44^64+1 = [11079795073, 1; 19997433904995365869542768320257176961, 1
29^72+1 = [2, 1; 17, 1; 673, 1; 26209, 1; 561377, 1; 11419906609, 1; 159959409668307793, 1; 51264663088279763377, 1; 371837256582239379457, 1
50^62+1 = [41, 1; 61, 1; 373, 1; 135781, 1; 7391269, 1; 40689754002142416245177, 1; 27912659223158460843311959393, 1
47^63-1 = [2, 1; 19, 1; 23, 1; 37, 1; 43, 1; 61, 1; 127, 1; 400681, 1; 256128979, 1; 567332587, 1; 2234786206087, 1; 218986325740360251685780429843, 1
47^63+1 = [2, 4; 3, 3; 7, 2; 103, 1; 3529, 1; 3691, 1; 5881, 1; 23227, 1; 95929, 1; 355321, 1; 973459, 1; 1794703, 1; 2155861, 1; 589101787, 1
57^60+1 = [2, 1; 601, 1; 1801, 1; 387169, 1; 5278001, 1; 287804929, 1; 10337608753481, 1; 1201095550676921, 1
20^81-1 = [19, 1; 421, 1; 64008001, 1; 150773239, 1; 879338701, 1; 298114935351301, 1; 7599707813206155097384225291, 1
20^81+1 = [3, 5; 7, 1; 109, 1; 127, 1; 163, 1; 307, 1; 4483, 1; 69481, 1; 99672121, 1; 1794112741, 1
18^84+1 = [113, 1; 929, 1; 3697, 1; 11019855601, 1; 361981632928757554946658433, 1
14^92+1 = [41, 1; 937, 1; 1657, 1; 726769322233, 1; 1355468392097, 1
42^65-1 = [11, 1; 41, 1; 53, 1; 181, 1; 1601, 1; 1602901, 1; 119999023, 1; 4852922309, 1; 34492551826295291, 1
42^65+1 = [43, 1; 131, 1; 18461, 1; 23201, 1; 120641, 1; 1153517, 1; 3473731, 1; 1381952443, 1; 367645736101541, 1
28^73-1 = [3, 3; 439, 1; 1924218827, 1; 1395719566812246425341583, 1; 33669332701243432328246627927, 1
28^73+1 = [29, 1; 877, 1; 1081277, 1; 361030699, 1; 8196570580777833295687571, 1
34^69-1 = [3, 2; 11, 1; 47, 1; 139, 1; 397, 1; 691, 1; 49957, 1; 65413, 1; 76039, 1; 11877483246539468276658679, 1
34^69+1 = [5, 1; 7, 1; 277, 1; 1123, 1; 349831, 1; 6527539, 1; 3985773656677, 1; 2332350350789787637, 1; 1200699736113456442159, 1
54^61-1 = [53, 1; 4637, 1; 32904029059528723344352074697, 1
54^61+1 = [5, 1; 11, 1; 13421, 1; 12447173, 1; 8072710111, 1
40^66+1 = [61, 1; 89, 1; 1601, 1; 2069, 1; 41941, 1; 409861, 1; 6398261, 1; 11926729, 1; 227551358517341, 1; 55847122150040300641, 1
21^80+1 = [2, 1; 1217, 1; 2689, 1; 31873, 1; 35201, 1; 6857635489, 1; 742519225358081, 1
45^64+1 = [2, 1; 1902641631856641539329, 1
58^60+1 = [41, 1; 2393, 1; 4729, 1; 20161, 1; 33409, 1; 190129, 1; 400003693899756583014833801, 1
17^86+1 = [2, 1; 5, 1; 29, 1; 173, 1; 2237, 1; 26673589, 1; 130246136377853, 1
13^95-1 = [2, 2; 3, 1; 191, 1; 27361, 1; 30941, 1; 4986361, 1; 12865927, 1; 9468940004449, 1
13^95+1 = [2, 1; 7, 1; 11, 1; 2411, 1; 19755615371, 1; 3657554614741, 1; 5810151294071, 1; 104422877883960436477, 1
38^67-1 = [37, 1; 269, 1; 1969519919767, 1; 58689823485624250571, 1
38^67+1 = [3, 1; 13, 1; 14071, 1; 3651271397, 1; 57485522291, 1; 1239965870454121, 1
15^90+1 = [2, 1; 13, 1; 37, 1; 113, 1; 3877, 1; 19421, 1; 33601, 1; 131381, 1; 278041, 1; 318601, 1; 706195561, 1; 2911460401, 1; 3506657472973, 1; 105091981250955481, 1
51^62+1 = [2, 1; 1301, 1
31^71-1 = [2, 1; 3, 1; 5, 1; 17609, 1; 611127785361198601, 1; 642443809919609072204778169817, 1
31^71+1 = [2, 5; 10603709, 1; 1331988009281919919112231122509158475284430963251, 1
48^63-1 = [13, 1; 47, 1; 71, 1; 181, 1; 31081, 1; 65701, 1; 186157, 1; 175926983, 1; 1687867926697, 1; 4712598196817449, 1; 11463867371190997981, 1
48^63+1 = [7, 3; 19, 1; 37, 1; 43, 1; 61, 1; 127, 1; 379, 1; 5209, 1; 5851, 1; 24571, 1; 42967, 1; 110017, 1; 645751, 1; 2807407, 1; 1711569511, 1; 3062033466409, 1; 600615109857751129, 1
22^79-1 = [3, 1; 7, 1
22^79+1 = [23, 1
26^75-1 = [5, 4; 11, 1; 19, 1; 37, 1; 8641, 1; 9661, 1; 317701, 1; 2906801, 1; 20785291, 1; 4315817869647001, 1; 45054418717916808461851, 1
26^75+1 = [3, 4; 7, 1; 31, 1; 151, 1; 431, 1; 1021, 1; 7951, 1; 28201, 1; 14346244151, 1; 216846518851, 1; 1727127900352201, 1; 9199235946217201, 1
19^83-1 = [2, 1; 3, 2; 167, 1
19^83+1 = [2, 2; 5, 1; 3980017, 1; 28615780547655601, 1
55^61-1 = [2, 1; 3, 3; 23867593, 1
55^61+1 = [2, 3; 7, 1; 733, 1; 755236898037041723, 1
43^65-1 = [2, 1; 3, 1; 7, 1; 131, 1; 2081, 1; 3500201, 1; 4479676558681871, 1; 40911050578149780601, 1
43^65+1 = [2, 2; 11, 1; 53, 1; 1301, 1; 3121, 1; 21841, 1; 55147, 1; 3341101, 1; 9093478224091, 1; 13361016018611, 1; 193075608041161, 1; 4654543684527542521, 1
23^78+1 = [2, 1; 5, 1; 37, 1; 53, 1; 157, 1; 7549, 1; 2861561, 1; 278640181, 1; 19243596061, 1; 3829141917458729, 1
59^60+1 = [2, 1; 17, 1; 241, 1; 593, 1; 601, 1; 58321, 1; 6890341821161, 1; 146830425486961, 1; 3128897838082361, 1; 25463693535122400344401, 1
24^77-1 = [23, 1; 29, 1; 67, 1; 239, 1; 7349, 1; 28771, 1; 136753, 1; 134367047, 1; 381000640372162273, 1; 3103766366465410644478943, 1
24^77+1 = [5, 2; 7393, 1; 183458857, 1; 60867245726761, 1
33^70+1 = [2, 1; 5, 2; 41, 1; 61, 1; 109, 1; 281, 1; 4721, 1; 23801, 1; 11001991508009041, 1; 1666359341086055617, 1
30^72+1 = [337, 1; 401, 1; 1297, 1; 4855073, 1; 532856497, 1; 807848290154833, 1
52^62+1 = [5, 1; 541, 1; 27199897, 1; 818040277, 1
46^64+1 = [944257, 1; 52208711297, 1; 6806175851393423565671196264598472321, 1
41^66+1 = [2, 1; 13, 1; 29, 2; 109, 1; 1277, 1; 1993, 1; 2377, 1; 3037, 1; 11174530093, 1; 296823196796698573, 1; 141002872158635579680840653413, 1
35^69-1 = [2, 1; 13, 1; 17, 1; 97, 1; 139, 1; 27739, 1; 51378407953, 1; 83212722673, 1; 2244479939269, 1; 715589319888957668605573, 1
35^69+1 = [2, 2; 3, 3; 47, 1; 397, 1; 8107823, 1; 98665447, 1; 338724757292881, 1; 23782658632422541223512211, 1
14^93-1 = [13, 1; 211, 1; 244898761, 1; 2472843559729, 1; 253445952598770930829423, 1; 3544762693352021265837373, 1
14^93+1 = [3, 2; 5, 1; 61, 1; 1613, 1; 3163, 1; 168269, 1; 7476844183, 1; 3519020880787, 1; 5329700081717383927, 1
39^67-1 = [2, 1; 19, 1; 1710181378935167809319928954519193424455741201, 1
39^67+1 = [2, 3; 5, 1; 11927, 1; 1447067, 1; 1077516868525091, 1; 8439745730700814436191, 1
37^68+1 = [2, 1; 89, 1; 10529, 1; 3378377, 1; 42066623761, 1; 5556078973369, 1
56^61-1 = [5, 1; 11, 1; 367, 1; 9029, 1
56^61+1 = [3, 1; 19, 1; 195085321, 1; 31301397367452880644774094242845020609837, 1
20^82+1 = [401, 1; 364984924121, 1; 42728337802653649, 1
60^60+1 = [17, 1; 41, 1; 281, 1; 521, 1; 2713, 1; 80449, 1; 44022001, 1; 828711601, 1; 2087802049, 1; 51680396161, 1; 1593657438236641, 1
18^85-1 = [17, 2; 41, 1; 1361, 1; 2711, 1; 3911, 1; 3462391, 1; 5124991, 1; 10275311, 1; 23718627631, 1; 7563707819165039903, 1
18^85+1 = [11, 1; 19, 1; 137, 1; 443, 1; 9041, 1; 35919131, 1; 1895634885375961, 1
29^73-1 = [2, 2; 7, 1; 6053603111, 1; 378491163256757, 1; 44615044785278167337, 1; 1776134532576692154401, 1
29^73+1 = [2, 1; 3, 1; 5, 1; 877, 1; 17315747, 1; 209981873, 1; 19102002081955131137, 1
44^65-1 = [43, 1; 53, 1; 131, 1; 313, 1; 4759, 1; 62297, 1; 126491, 1; 3835261, 1; 10955023, 1; 992079791, 1
44^65+1 = [3, 2; 5, 2; 421, 1; 1741, 1; 18539, 1; 2777064559610927, 1; 6962625655637855802110187911, 1
53^62+1 = [2, 1; 5, 1; 281, 1; 92440192126938595012573, 1; 93510080383641146298112331285100865253, 1
13^96+1 = [2, 1; 193, 1; 1153, 1; 1601, 1; 10433, 1; 68675120456139881482562689, 1; 11352931040252580224415980746369, 1
47^64+1 = [2, 1; 634241, 1; 1393921, 1; 596367067316360449, 1
15^91-1 = [2, 1; 7, 2; 53, 1; 911, 1; 157483, 1; 1743463, 1; 16655159, 1; 24002161, 1; 124074497, 1; 936800875930739, 1
15^91+1 = [2, 4; 79, 1; 3706067, 1; 10678711, 1; 1539711288259, 1; 94672331640797, 1; 10640666506292551, 1
50^63-1 = [7, 3; 127, 1; 631, 1; 2017, 1; 2551, 1; 165817, 1; 1104097, 1; 10290337, 1; 2277696793, 1; 15625125001, 1; 21773059085233, 1
50^63+1 = [3, 3; 17, 1; 19, 1; 43, 1; 211, 1; 6091, 1; 6427, 1; 28603, 1; 182089, 1; 2514961, 1; 28352991619, 1; 183630997877083, 1
17^87-1 = [2, 4; 59, 1; 307, 1; 523, 1; 7193, 1; 8179, 1; 16879, 1; 6088087, 1; 37286983, 1; 52627759112497, 1; 11658852700685942029849, 1
17^87+1 = [2, 1; 3, 3; 7, 1; 13, 1; 349, 1; 23549, 1; 53593, 1; 2919779, 1; 15598057, 1; 18032534719, 1; 61878754061, 1
28^74+1 = [5, 1; 157, 1
21^81-1 = [2, 2; 5, 1; 109, 1; 163, 1; 463, 1; 4779433, 1; 85775383, 1; 7429452749713, 1
21^81+1 = [2, 1; 11, 1; 19, 1; 37, 1; 199, 1; 421, 1; 613, 1; 1783, 1; 5077, 1; 17497, 1; 110323, 1; 7101932659132249, 1
57^61-1 = [2, 3; 7, 1; 8297, 1; 275599, 1; 454102852372034133722600077, 1
57^61+1 = [2, 1; 29, 1; 977, 1; 431898667, 1; 3519003390903618764755673, 1; 20500212815560871346128284471, 1
42^66+1 = [5, 1; 89, 1; 353, 1; 673, 1; 3301, 1; 4621, 1; 63361, 1; 1418881993, 1; 36440252058534413, 1
34^70+1 = [13, 1; 89, 1; 281, 1; 6581, 1; 24893280301, 1; 97600331641, 1; 1784250435661, 1; 1065635017297481, 1; 8485260107435861, 1
40^67-1 = [3, 1; 13, 1; 1609, 1; 27477907, 1; 353559835357, 1
40^67+1 = [41, 1
31^72+1 = [2, 1; 17, 1; 97, 1; 1704673, 1; 476428033, 1; 25085030513, 1; 18210235769136721, 1; 7499207440683838894753, 1
22^80+1 = [449, 1; 180001, 1; 2310689, 1; 2902518892577, 1; 9621842168443061282218081, 1
54^62+1 = [2917, 1; 4458230758773551238806221, 1
19^84+1 = [2, 1; 17, 1; 3833, 1; 4297, 1; 3952393, 1; 4898725341275828472027787456561, 1
38^68+1 = [41, 1; 50857, 1; 2214026043915374579009716433, 1
45^65-1 = [2, 2; 11, 1; 131, 1; 1471, 1; 2851, 1; 48491, 1; 374665201, 1; 411590401, 1; 1436796791, 1; 85127742311, 1; 1987607593147801, 1
45^65+1 = [2, 1; 23, 1; 41, 1; 2003, 1; 97841, 1; 2529229, 1; 13314833663, 1; 13941960463051394148848528041003476421, 1
26^76+1 = [17, 1; 26881, 1; 5548489897, 1; 25320232858838841728481328217, 1; 8751329810753593058093497033897, 1
58^61-1 = [3, 1; 19, 1; 733, 1; 90559148201, 1
58^61+1 = [59, 1; 3295264409, 1; 7192041338831, 1; 82283126277816266983540643657458661879089, 1
23^79-1 = [2, 1; 11, 1; 317, 1; 5605051, 1; 17510351, 1; 1711849421, 1; 5308250621847606803, 1
23^79+1 = [2, 3; 3, 1; 29863, 1
51^63-1 = [2, 1; 5, 2; 7, 2; 379, 1; 3697, 1; 11411, 1; 34147, 1; 132679, 1; 1572887, 1; 17596420453, 1; 647186213288917, 1; 11729992239855919, 1
51^63+1 = [2, 2; 13, 1; 19, 1; 29, 1; 43, 1; 71, 1; 127, 1; 421, 1; 463, 1; 2551, 1; 40111, 1; 1278817, 1; 48461449, 1; 290685529, 1; 926113429, 1
48^64+1 = [417813806500107334422529, 1; 171384369229251163605657601, 1
24^78+1 = [13, 2; 73, 1; 157, 1; 313, 1; 349, 1; 577, 1; 20749, 1; 128857, 1; 95795485657, 1; 30030953107741, 1; 2136732643031689, 1; 4140359222873146573, 1
14^94+1 = [197, 1; 123517, 1; 23688237358867852955597637113063638372710957829, 1
43^66+1 = [2, 1; 5, 2; 37, 1; 6337, 1; 15973, 1; 53593, 1; 568657, 1; 3416953, 1; 29224547986227053551568061157, 1
33^71-1 = [2, 5; 569, 1; 2557, 1; 5187971, 1; 70643723, 1; 1067881020542521, 1; 2293884580685623957, 1; 95535853750558053319843, 1
33^71+1 = [2, 1; 17, 1; 6108983, 1; 3648534830043396481338793, 1
30^73-1 = [29, 1; 500606982978582492107, 1
30^73+1 = [31, 1; 6133, 1; 1305971, 1; 9303851, 1; 6154752013844260765111, 1; 4978667413900828078949549, 1
55^62+1 = [2, 1; 17, 1; 89, 1; 1240484071201, 1; 40420782181701941, 1; 60020439454964647806557, 1
18^86+1 = [5, 2; 13, 1; 173, 1; 8429, 1; 9581702213, 1; 43983075563266931110717441203192765085093, 1
20^83-1 = [19, 1; 27817851030769, 1; 2871487521092731391, 1; 414249085636225553185611071, 1
20^83+1 = [3, 1; 7, 1; 167, 1; 343289, 1; 9625843, 1
59^61-1 = [2, 1; 29, 1; 367, 1; 2441, 1; 54413, 1; 436273, 1
59^61+1 = [2, 2; 3, 1; 5, 1; 1370463715775395663123263267401737793110333036357, 1
13^97-1 = [2, 2; 3, 1; 389, 1; 971, 1; 93964390627, 1
13^97+1 = [2, 1; 7, 1; 404094629, 1
41^67-1 = [2, 3; 5, 1; 269, 1; 466723, 1; 862559, 1; 168225209, 1; 196633877057848946743623103, 1; 77245547442917125165296411739, 1
41^67+1 = [2, 1; 3, 1; 7, 1; 317179, 1
46^65-1 = [3, 2; 5, 2; 53, 1; 79, 1; 131, 1; 157, 1; 547, 1; 24077, 1; 915391, 1; 10598563, 1; 51789947431, 1; 21743939130811, 1
46^65+1 = [11, 1; 31, 1; 47, 1; 71, 1; 181, 1; 7411, 1; 209327, 1; 419690080437473, 1
35^70+1 = [2, 1; 181, 1; 613, 1; 305369, 1; 12431152621, 1; 147808623761, 1; 11056997307329, 1
52^63-1 = [3, 3; 17, 1; 29, 1; 43, 1; 127, 1; 337, 1; 919, 1; 991, 1; 1303, 1; 1583, 1; 5209, 1; 8191, 1; 52363, 1; 1597597, 1; 1071321931, 1; 3254599129712990747437, 1
52^63+1 = [7, 2; 19, 1; 53, 1; 379, 1; 1195489, 1; 4327093, 1; 1040551003, 1; 19397579293, 1; 47606465238403, 1; 37902864152944874310575419, 1
39^68+1 = [2, 1; 953, 1; 1156721, 1; 150946477016946024834952969, 1
15^92+1 = [2, 1; 17, 1; 1489, 1
37^69-1 = [2, 2; 3, 3; 7, 1; 47, 1; 67, 1; 139, 1; 2224147, 1; 1845029930335901, 1; 375176717285846681, 1
37^69+1 = [2, 1; 19, 1; 31, 1; 43, 1; 397073, 1; 1495231, 1; 3600283, 1; 88578337, 1; 1555898389, 1; 33365387742119, 1; 469773284253201926058667, 1
29^74+1 = [2, 1; 421, 1; 593, 1; 18353, 1; 32117, 1; 940705857471173, 1
17^88+1 = [2, 1; 18913, 1; 184417, 1
56^62+1 = [373, 1; 3137, 1; 22817, 1; 5118101, 1; 3386129009, 1; 2378055944233, 1; 550386339795388324920941723693, 1
21^82+1 = [2, 1; 13, 1; 17, 1; 153065748541, 1; 166149756476309, 1; 294168762061816395873078148041249581, 1
60^61-1 = [59, 1; 7687, 1; 20979773866271054688241, 1
60^61+1 = [61, 2; 22742387, 1; 1039052667517004801929647383, 1; 2372500211008333003222944301, 1
44^66+1 = [13, 1; 149, 1; 1753, 1; 2137, 1; 46993, 1; 1006897, 1; 2269900598417, 1; 325703497841450045153, 1
28^75-1 = [3, 4; 31, 1; 271, 1; 15101, 1; 15991, 1; 36901, 1; 106801, 1; 637421, 1; 734941, 1; 6813064001, 1; 7984305701, 1; 171813927594772108174052851, 1
28^75+1 = [11, 1; 29, 1; 151, 1; 757, 1; 4621, 1; 53951, 1; 2606251, 1; 39148201, 1; 84673681, 1; 222929435014083414901, 1
53^63-1 = [2, 2; 7, 2; 13, 1; 29, 1; 37, 1; 43, 1; 163, 1; 307, 1; 409, 1; 3907, 1; 11971, 1; 210421, 1; 511509937, 1; 778986167, 1; 3130547197, 1
53^63+1 = [2, 1; 3, 5; 19, 1; 127, 1; 673, 1; 919, 1; 2647, 1; 319411, 1; 1360423, 1; 32323789, 1; 388845829, 1; 315473447928619, 1; 189091264897987327, 1
47^65-1 = [2, 1; 11, 1; 23, 1; 31, 1; 53, 1; 2237, 1; 14621, 1; 14050609, 1; 71265169, 1; 972341761, 1; 17092615411, 1; 33244291081, 1
47^65+1 = [2, 4; 3, 1; 131, 1; 911, 1; 12377, 1; 372061, 1; 4778021, 1; 2273761751, 1; 70168829040103, 1
19^85-1 = [2, 1; 3, 2; 151, 1; 911, 1; 3044803, 1; 12299588826871, 1; 99995282631947, 1; 4091790564972909948701, 1
19^85+1 = [2, 2; 5, 2; 11, 1; 2251, 1; 140495619966101, 1; 274019342889240109297, 1; 693128329340299192949731, 1
50^64+1 = [257, 1; 30977, 1; 37633, 1
34^71-1 = [3, 1; 11, 1; 1279, 1; 575243, 1; 276394318547, 1
34^71+1 = [5, 1; 7, 1; 569, 1; 853, 1; 1847, 1; 2699, 1; 2862814878908925903954231791, 1
22^81-1 = [3, 5; 7, 1; 13, 2; 109, 1; 127, 1; 163, 1; 433, 1; 297613, 1; 2558953, 1; 5499494353, 1; 24678723493, 1; 59780311093, 1
22^81+1 = [19, 1; 23, 1; 463, 1; 811, 1; 3187, 1; 144667, 1; 1066231, 1; 5966803, 1; 2964868327, 1