Ultra-high Energy Cosmic Ray

You have: mega ton tnt
You want: eV
	* 2.6114477e+34

Could a single very high energy proton wipe out an entire city? The highest energy cosmic ray ever recorded (the Fly's Eye Event) was 3.2e20 eV, so we are still 14 orders of magnitude away.

You have: 3.2e20 eV
You want: mg tnt
        * 11.116406

Mandelbright

If each point outside the Mandelbrot set radiated proportional to escape time, would the total brightness be finite? -- Mobile Email from a Cingular Wireless Customer http://www.cingular.com

Optical Illusions Etc...

Optical Illusions Etc...

md5sum and sha1sum of zeros

The file size is 10737418240.

% dd if=/dev/zero of=ztest bs=1k count=10M
10485760+0 records in
10485760+0 records out
% md5sum /tmp/ztest
2dd26c4d4799ebd29fa31e48d49e8e53  /tmp/ztest
% sha1sum /tmp/ztest
a0b6e2ca4e28360a929943e8eb966f703a69dc44  /tmp/ztest

Now, with 2,000,000,000 byte files (avoiding the maximum file size limitation):

% dd if=/dev/zero bs=1000 count=2000000 | md5sum
2000000+0 records in
2000000+0 records out
5ab9550b6548d740cc7713661f22e9af  -
% dd if=/dev/zero bs=1000 count=2000000 | sha1sum
2000000+0 records in
2000000+0 records out
752ef2367f479e79e4f0cded9c270c2890506ab0  -

factorint precprime

The factorization of the integer preceding the first prime less than a given power of two.

? for(i=3,1000,print(i," ",factorint(precprime(2^i)-1)," ",gettime()))

exponent	preceding prime	factorization	milliseconds
3	-1	[2, 1; 3, 1]	0
4	-3	[2, 2; 3, 1]	0
5	-1	[2, 1; 3, 1; 5, 1]	0
6	-3	[2, 2; 3, 1; 5, 1]	0
7	-1	[2, 1; 3, 2; 7, 1]	0
8	-5	[2, 1; 5, 3]	0
9	-3	[2, 2; 127, 1]	0
10	-3	[2, 2; 3, 1; 5, 1; 17, 1]	0
11	-9	[2, 1; 1019, 1]	0
12	-3	[2, 2; 3, 1; 11, 1; 31, 1]	0
13	-1	[2, 1; 3, 2; 5, 1; 7, 1; 13, 1]	0
14	-3	[2, 2; 3, 2; 5, 1; 7, 1; 13, 1]	0
15	-19	[2, 2; 3, 1; 2729, 1]	0
16	-15	[2, 4; 3, 2; 5, 1; 7, 1; 13, 1]	0
17	-1	[2, 1; 3, 1; 5, 1; 17, 1; 257, 1]	0
18	-5	[2, 1; 53, 1; 2473, 1]	0
19	-1	[2, 1; 3, 3; 7, 1; 19, 1; 73, 1]	0
20	-3	[2, 2; 3, 3; 7, 1; 19, 1; 73, 1]	0
21	-9	[2, 1; 1048571, 1]	0
22	-3	[2, 2; 3, 1; 5, 2; 11, 1; 31, 1; 41, 1]	0
23	-15	[2, 4; 524287, 1]	0
24	-3	[2, 2; 3, 1; 23, 1; 89, 1; 683, 1]	0
25	-39	[2, 3; 29, 1; 61, 1; 2371, 1]	0
26	-5	[2, 1; 479, 1; 70051, 1]	0
27	-39	[2, 3; 11, 1; 101, 1; 15101, 1]	0
28	-57	[2, 1; 3, 1; 7, 1; 11, 1; 581029, 1]	0
29	-3	[2, 2; 7, 1; 73, 1; 262657, 1]	0
30	-35	[2, 2; 7, 1; 2341, 1; 16381, 1]	0
31	-1	[2, 1; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1; 331, 1]	0
32	-5	[2, 1; 5, 1; 19, 1; 22605091, 1]	0
33	-9	[2, 1; 4294967291, 1]	10
34	-41	[2, 1; 79, 1; 108733349, 1]	0
35	-31	[2, 5; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1; 331, 1]	0
36	-5	[2, 1; 5, 1; 6871947673, 1]	0
37	-25	[2, 1; 3, 1; 15473, 1; 1480417, 1]	0
38	-45	[2, 1; 3, 1; 7, 2; 233, 1; 409, 1; 9811, 1]	0
39	-7	[2, 3; 3, 3; 5, 1; 7, 1; 13, 1; 19, 1; 37, 1; 73, 1; 109, 1]	0
40	-87	[2, 3; 3, 2; 1487, 1; 10269667, 1]	0
41	-21	[2, 1; 5, 1; 43, 1; 5939, 1; 861089, 1]	0
42	-11	[2, 2; 13, 1; 84577817521, 1]	10
43	-57	[2, 1; 5, 2; 7, 1; 23, 1; 1092682363, 1]	0
44	-17	[2, 1; 7, 1; 4583, 1; 7993, 1; 34303, 1]	0
45	-55	[2, 3; 3, 1; 19, 1; 77158710721, 1]	0
46	-21	[2, 1; 3, 1; 263, 1; 44593627489, 1]	0
47	-115	[2, 2; 3, 1; 7, 1; 1675446289943, 1]	10
48	-59	[2, 2; 797, 1; 2459, 1; 35905663, 1]	0
49	-81	[2, 1; 5, 1; 223, 1; 252443925301, 1]	10
50	-27	[2, 2; 3, 1; 6637, 1; 40123, 1; 352333, 1]	0
51	-129	[2, 1; 701, 1; 1531, 1; 1049075089, 1]	0
52	-47	[2, 4; 11, 1; 167, 1; 239, 1; 641110271, 1]	10
53	-111	[2, 4; 5, 1; 61, 1; 23563, 1; 78332027, 1]	0
54	-33	[2, 1; 3, 1; 5, 2; 486391, 1; 246912443, 1]	0
55	-55	[2, 3; 3, 3; 709, 1; 235260911423, 1]	10
56	-5	[2, 1; 5, 1; 1871, 1; 2207, 1; 2621, 1; 665789, 1]	0
57	-13	[2, 1; 3, 1; 24019198012642643, 1]	0
58	-27	[2, 2; 3, 1; 24019198012642643, 1]	0
59	-55	[2, 3; 3, 1; 24019198012642643, 1]	10
60	-93	[2, 1; 3, 1; 31, 1; 375983, 1; 16486124939, 1]	10
61	-1	[2, 1; 3, 2; 5, 2; 7, 1; 11, 1; 13, 1; 31, 1; 41, 1; 61, 1; 151, 1; 331, 1; 1321, 1]	0
62	-57	[2, 1; 3, 2; 1289, 1; 198762435067123, 1]	0
63	-25	[2, 1; 3, 4; 17, 1; 23, 1; 319279, 1; 456065899, 1]	10
64	-59	[2, 2; 11, 1; 137, 1; 547, 1; 5594472617641, 1]	0
65	-49	[2, 1; 3, 3; 47, 1; 3384529, 1; 4294967291, 1]	10
66	-5	[2, 1; 47, 1; 239831, 1; 3273004044197, 1]	0
67	-19	[2, 2; 3, 2; 1409, 1; 2909351640045667, 1]	10
68	-23	[2, 3; 47, 1; 239831, 1; 3273004044197, 1]	0
69	-19	[2, 2; 3, 1; 41, 1; 239, 1; 5020034445340559, 1]	10
70	-35	[2, 2; 13, 1; 463, 1; 5113, 1; 2854273, 1; 3360037, 1]	0
71	-231	[2, 3; 709, 1; 185123, 1; 2248708131661, 1]	10
72	-93	[2, 1; 3, 1; 251, 1; 3135701515849698017, 1]	10
73	-69	[2, 1; 17, 1; 31, 1; 8960847216071433043, 1]	0
74	-35	[2, 2; 61, 1; 523, 1; 242819, 1; 283007, 1; 2154013, 1]	10
75	-97	[2, 1; 3, 2; 5, 1; 11, 1; 23, 1; 157, 1; 4229021, 1; 2498890063, 1]	10
76	-15	[2, 4; 3, 3; 5, 1; 7, 1; 13, 1; 17, 1; 19, 1; 37, 1; 73, 1; 109, 1; 241, 1; 433, 1; 38737, 1]	0
77	-33	[2, 1; 613, 1; 14629, 1; 70729, 1; 135559, 1; 878777, 1]	10
78	-11	[2, 2; 13, 1; 21407, 1; 271506673682994863, 1]	10
79	-67	[2, 2; 3, 1; 5, 1; 29, 1; 347392476900755509973, 1]	0
80	-65	[2, 1; 5, 1; 19, 1; 283, 1; 2192857859, 1; 10252956977, 1]	40
81	-51	[2, 2; 5, 2; 24178516392292583494123, 1]	10
82	-57	[2, 1; 3, 1; 7, 1; 115135792344250397591063, 1]	10
83	-55	[2, 3; 3, 1; 1873, 1; 6247, 1; 98299, 1; 540877, 1; 647771, 1]	10
84	-35	[2, 2; 5, 1; 7, 1; 23, 1; 139, 1; 687839617, 1; 62829235873, 1]	10
85	-19	[2, 2; 3, 2; 926902397, 1; 1159346153407711, 1]	50
86	-35	[2, 2; 47, 1; 193, 1; 307, 1; 4463, 1; 108637, 1; 14325884401, 1]	10
87	-67	[2, 2; 3, 1; 5, 1; 109, 1; 23473, 1; 328687, 1; 3066766765499, 1]	10
88	-299	[2, 2; 11, 1; 23, 1; 2617, 1; 116857175046309048289, 1]	10
89	-1	[2, 1; 3, 1; 5, 1; 17, 1; 23, 1; 89, 1; 353, 1; 397, 1; 683, 1; 2113, 1; 2931542417, 1]	0
90	-33	[2, 1; 3, 1; 5, 1; 11, 1; 3751333452379940226967043, 1]	10
91	-45	[2, 1; 11, 1; 479, 1; 5237, 1; 8753, 1; 173357, 1; 29565860677, 1]	10
92	-83	[2, 2; 17, 1; 43, 1; 7649, 1; 30161, 1; 49639, 1; 147879785303, 1]	0
93	-25	[2, 1; 3, 2; 550195573015724566621832987, 1]	10
94	-3	[2, 2; 3, 1; 5, 1; 47, 1; 277, 1; 1013, 1; 1657, 1; 30269, 1; 178481, 1; 2796203, 1]	10
95	-15	[2, 4; 127, 1; 911, 1; 8191, 1; 112901153, 1; 23140471537, 1]	10
96	-17	[2, 1; 17, 1; 41, 1; 2503, 1; 11927401, 1; 1903750979809649, 1]	30
97	-141	[2, 1; 5, 1; 7, 1; 30427, 1; 421493, 1; 176507042656349189, 1]	50
98	-51	[2, 2; 3, 1; 11489, 1; 2298667203825814187296369, 1]	10
99	-115	[2, 2; 3, 2; 11, 1; 23, 1; 103, 1; 216901, 1; 3114926258434939853, 1]	10
100	-15	[2, 4; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 97, 1; 193, 1; 241, 1; 257, 1; 673, 1; 65537, 1; 22253377, 1]	10
101	-69	[2, 1; 2733092861843, 1; 463815415102075087, 1]	150
102	-33	[2, 1; 3, 1; 5, 1; 3319, 1; 15761, 1; 3231076804495048272311, 1]	10
103	-97	[2, 1; 3, 1; 5, 1; 19, 1; 17174671, 1; 131111671, 1; 7901051977843, 1]	130
104	-17	[2, 1; 7, 1; 17, 1; 85220208418704497579610299521, 1]	10
105	-13	[2, 1; 3, 1; 37, 2; 47, 1; 20773, 1; 26497, 1; 25507717, 1; 7483925773, 1]	10
106	-117	[2, 1; 3, 1; 2593891, 1; 5212866077423626108151101, 1]	30
107	-1	[2, 1; 3, 1; 107, 1; 6361, 1; 69431, 1; 20394401, 1; 28059810762433, 1]	10
108	-59	[2, 2; 1233003839411, 1; 65798366413329190859, 1]	160
109	-31	[2, 5; 3, 1; 5, 1; 17, 1; 53, 1; 157, 1; 1613, 1; 2731, 1; 8191, 1; 858001, 1; 308761441, 1]	10
110	-21	[2, 1; 3, 2; 29, 1; 149, 1; 19801, 1; 842860357178749786904309, 1]	10
111	-37	[2, 1; 3, 1; 5, 1; 8209, 1; 10541878544960465400841548563, 1]	0
112	-75	[2, 2; 3, 1; 5, 1; 8209, 1; 10541878544960465400841548563, 1]	10
113	-133	[2, 1; 3, 1; 249229, 1; 6944479252059789228019875067, 1]	20
114	-11	[2, 2; 13, 1; 12853, 1; 31075037007432132746802580237, 1]	0
115	-67	[2, 2; 3, 1; 5, 2; 353, 1; 96233, 1; 60884249347, 1; 66945988795223, 1]	70
116	-3	[2, 2; 3, 2; 7, 1; 571, 1; 32377, 1; 174763, 1; 524287, 1; 1212847, 1; 160465489, 1]	20
117	-279	[2, 3; 20769187434139310514121985316880349, 1]	20
118	-5	[2, 1; 29, 1; 4729, 1; 264331, 1; 120282553, 1; 38105831644971763, 1]	70
119	-69	[2, 1; 29, 1; 344064569, 1; 33304394189535351753233609, 1]	220
120	-119	[2, 3; 7, 1; 17, 1; 107, 2; 443, 1; 588365753, 1; 467890108350253093, 1]	90
121	-73	[2, 1; 3, 2; 71, 1; 1063, 1; 183033847, 1; 10691384514931340478341, 1]	160
122	-3	[2, 2; 3, 2; 5, 2; 7, 1; 11, 1; 13, 1; 17, 1; 31, 1; 41, 1; 61, 1; 151, 1; 241, 1; 331, 1; 1321, 1; 61681, 1; 4562284561, 1]	10
123	-67	[2, 2; 3, 1; 5, 1; 47, 1; 109, 1; 34595041857893574673792883343883, 1]	10
124	-59	[2, 2; 11, 1; 2633, 1; 11285865197, 1; 16266011243783873888999, 1]	290
125	-9	[2, 1; 11, 1; 19, 1; 101, 1; 75611, 1; 25593610799, 1; 520637276195190611, 1]	110
126	-137	[2, 1; 317, 1; 3919, 1; 199974079, 1; 171214770098900531773639, 1]	150
127	-1	[2, 1; 3, 3; 7, 2; 19, 1; 43, 1; 73, 1; 127, 1; 337, 1; 5419, 1; 92737, 1; 649657, 1; 77158673929, 1]	10
128	-159	[2, 5; 3, 1; 10253, 1; 29333, 1; 4454477, 1; 42113237, 1; 62826870453001, 1]	190
129	-25	[2, 1; 3, 2; 23, 1; 53, 1; 2207, 1; 73037, 1; 192419007647917553731343987, 1]	10
130	-5	[2, 1; 23, 1; 32985101, 1; 897064739519922787230182993783, 1]	60
131	-69	[2, 1; 19, 1; 20219, 1; 59351, 1; 59697771913750598441845212299, 1]	10
132	-347	[2, 2; 4086621307, 1; 333069635141447143111442312491, 1]	800
133	-99	[2, 2; 7, 1; 17, 1; 2447, 1; 23605948748323511, 1; 396029047604911001, 1]	300
134	-45	[2, 1; 3, 1; 7, 1; 443, 1; 4241, 1; 275993039834493705010208653191503, 1]	10
135	-45	[2, 1; 359, 1; 354034717, 1; 171348031280966828492853945787, 1]	120
136	-113	[2, 1; 7, 1; 35023, 1; 177663425120146040044346163342727151, 1]	20
137	-13	[2, 1; 3, 2; 15493, 1; 12611483, 1; 49537629558702115833889161799, 1]	20
138	-105	[2, 1; 3, 1; 7, 1; 17, 1; 19, 1; 283, 1; 131267, 1; 355111, 1; 8336660597, 1; 233555095796839, 1]	80
139	-187	[2, 2; 3, 1; 5, 2; 571, 1; 13218581, 1; 307770647134532760329414930789, 1]	60
140	-27	[2, 2; 3, 1; 1406497, 1; 830370383, 1; 99450617953977436093324829, 1]	490
141	-9	[2, 1; 2039, 1; 483241756040154301, 1; 1414548079303981253089, 1]	840
142	-111	[2, 4; 3, 1; 1406497, 1; 830370383, 1; 99450617953977436093324829, 1]	490
143	-69	[2, 1; 23, 1; 31, 1; 131, 1; 353, 1; 8893, 1; 177755497, 1; 277728329, 1; 385152161919299, 1]	410
144	-83	[2, 2; 1700143, 1; 3279245510308636264940025379136984581, 1]	20
145	-151	[2, 3; 3, 1; 5, 1; 67, 1; 798006697591, 1; 6951632199463154252028137287, 1]	750
146	-153	[2, 1; 3, 1; 5, 1; 491, 1; 6055871065452986596479489008186927768087, 1]	30
147	-145	[2, 1; 3, 1; 34301, 1; 161233, 1; 417523, 1; 174323135449, 1; 73868956290836867, 1]	150
148	-167	[2, 3; 11, 1; 19, 1; 132657971690831, 1; 1608680259113069994569276309, 1]	1730
149	-31	[2, 5; 3, 3; 5, 1; 7, 1; 13, 1; 17, 1; 19, 1; 37, 1; 73, 1; 97, 1; 109, 1; 241, 1; 257, 1; 433, 1; 577, 1; 673, 1; 38737, 1; 487824887233, 1]	10
150	-3	[2, 2; 3, 1; 5, 1; 149, 1; 223, 1; 593, 1; 1777, 1; 25781083, 1; 184481113, 1; 231769777, 1; 616318177, 1]	170
151	-195	[2, 2; 17, 1; 41977873314881172972302528513220445187727839, 1]	30
152	-17	[2, 1; 7, 1; 17, 1; 62983, 1; 4991839, 1; 44227633, 1; 1725062259481544383088761, 1]	160
153	-69	[2, 1; 13, 1; 17, 1; 31, 1; 833307658856201944859603543686758217126111, 1]	20
154	-243	[2, 2; 3, 1; 5, 1; 13, 1; 1451, 1; 8093, 1; 81727, 1; 1208758919, 1; 25237278936719029457687, 1]	140
155	-31	[2, 5; 3, 2; 7, 1; 11, 1; 31, 1; 151, 1; 251, 1; 331, 1; 601, 1; 1801, 1; 4051, 1; 100801, 1; 10567201, 1; 1133836730401, 1]	40
156	-143	[2, 4; 13, 1; 19, 1; 21407, 1; 271506673682994863, 1; 3976729669784964390481, 1]	920
157	-19	[2, 2; 3, 2; 565013, 1; 283127627, 1; 31722406732365708246533232867557, 1]	1230
158	-15	[2, 4; 3, 1; 23, 1; 43, 1; 89, 1; 127, 1; 617, 1; 683, 1; 78233, 1; 35532364099, 1; 581283643249112959, 1]	70
159	-91	[2, 2; 3, 1; 7, 1; 453553, 1; 84301218091, 1; 227524480117462744571759085503, 1]	1360
160	-47	[2, 4; 71, 1; 40813, 1; 82963182251, 1; 379959277835395773058806460021, 1]	1450
161	-159	[2, 5; 181, 1; 1609, 1; 15991, 1; 209060319214451, 1; 93820441463831721806779, 1]	570
162	-101	[2, 1; 307, 1; 12209275712633, 1; 779831951475688142994810611932471, 1]	6760
163	-55	[2, 3; 3, 3; 46020829, 1; 230938061, 1; 5093139709090657290362849823763, 1]	200
164	-63	[2, 6; 3, 1; 2687, 1; 202029703, 1; 1113491139767, 1; 201487636602438195784363, 1]	510
165	-25	[2, 1; 3, 2; 181, 1; 43913, 1; 458336239, 1; 713215708842851814477991561387801, 1]	70
166	-5	[2, 1; 59573573, 1; 3218926687654133, 1; 243884697112256951372125781, 1]	1580
167	-135	[2, 3; 2863345019, 1; 8166681291331467970489433122505775233821, 1]	590
168	-257	[2, 1; 1385887, 1; 354062624131, 1; 381242554710766547265379727561867, 1]	4270
169	-643	[2, 2; 3, 1; 11, 1; 2287, 1; 2478729705162984106876438083339086887890174577, 1]	90
170	-143	[2, 4; 5, 1; 7, 1; 11, 1; 197, 1; 263, 1; 31177, 1; 69439, 1; 4323551, 1; 54561836281, 1; 9181829646439421, 1]	100
171	-19	[2, 2; 3, 1; 373, 1; 100271, 1; 6669047866104325500594787895587024454736043, 1]	20
172	-95	[2, 5; 5, 2; 239, 1; 1061, 1; 15263, 1; 1933374909205041859345518705365754560881, 1]	30
173	-55	[2, 3; 3, 1; 53, 1; 811, 1; 296269, 1; 2409986827785043447, 1; 16254754097798812024831, 1]	930
174	-3	[2, 2; 3, 1; 5, 1; 173, 1; 431, 1; 9719, 1; 101653, 1; 500177, 1; 2099863, 1; 1759217765581, 1; 2932031007403, 1]	90
175	-229	[2, 1; 3, 1; 11, 1; 17, 1; 433, 1; 5303, 1; 1441548550921, 1; 12894888372628703287173138978851, 1]	2980
176	-233	[2, 1; 19, 1; 100390812696683, 1; 25107395873362030653452226162419112763, 1]	17300
177	-339	[2, 2; 43, 1; 443, 1; 269897, 1; 43417999, 1; 214540455246546428451705911111471989, 1]	170
178	-41	[2, 1; 38461, 1; 4980680237337461514125825599796902003388949592391, 1]	40
179	-49	[2, 1; 3, 2; 11, 1; 197, 1; 641, 1; 9619, 1; 30809, 1; 189875706144165757, 1; 544631616422353800199, 1]	880
180	-47	[2, 4; 107, 1; 5920151, 1; 47545643, 1; 12399411469, 1; 256478448539413317884593007, 1]	730
181	-165	[2, 1; 41, 1; 173, 1; 33861401473, 1; 6380641301623404260293530023063493488537, 1]	1740
182	-161	[2, 1; 431, 1; 7639, 1; 669102391, 1; 40934005122337, 1; 33989017713868288731201457, 1]	730
183	-147	[2, 2; 5, 1; 7, 1; 523, 1; 887, 1; 1035237779553371216351, 1; 182345793684253747191714659, 1]	6940
184	-33	[2, 1; 3, 2; 347, 1; 32143427003, 1; 122130755781316693861449472063856783957039, 1]	2950
185	-303	[2, 4; 7100671, 1; 431648090966582977399839262275441062856943835923, 1]	80
186	-371	[2, 2; 7, 1; 11, 1; 373, 1; 881, 1; 14321, 1; 67665982492050085897207378640217002088350963, 1]	70
187	-85	[2, 1; 3, 1; 7, 2; 84017, 1; 108161, 1; 14839871, 1; 16207518253569833, 1; 305265236392825045873, 1]	510
188	-125	[2, 1; 5, 1; 13, 1; 397, 1; 1918919364716236391465881, 1; 3961399114926731715517839373, 1]	23570
189	-25	[2, 1; 3, 3; 1227563, 1; 524793072442523, 1; 22555036659659199150862565259671041, 1]	13800
190	-11	[2, 2; 11, 1; 4668159781, 1; 243343180651407107, 1; 31396526753320467221701278169, 1]	6770
191	-19	[2, 2; 3, 1; 13, 1; 13757, 1; 3944813, 1; 379007533686944959, 1; 978152507894592399617628427, 1]	4150
192	-237	[2, 1; 3, 1; 15739, 1; 309479, 1; 1142678623, 1; 187964352975314705242455686948494766561, 1]	110
193	-31	[2, 5; 3, 1; 5, 1; 283, 1; 2351, 1; 3761, 1; 4513, 1; 13264529, 1; 7484047069, 1; 165768537521, 1; 140737471578113, 1]	770
194	-33	[2, 1; 3, 1; 5, 2; 109, 1; 1120993, 1; 1369930393629556067951295927819449355800614521121, 1]	40
195	-135	[2, 3; 7649737, 1; 2452958806703, 1; 334520246557246643906364340768470860089, 1]	20650
196	-15	[2, 4; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 97, 1; 193, 1; 241, 1; 257, 1; 641, 1; 673, 1; 65537, 1; 6700417, 1; 22253377, 1; 18446744069414584321, 1]	120
197	-75	[2, 2; 137, 1; 577, 1; 6037, 1; 117496859, 1; 895581969324648364417023941445052237459747, 1]	220
198	-17	[2, 1; 5647, 1; 6268111, 1; 5674853826681942056754247728019406574089602588439, 1]	80
199	-49	[2, 1; 3, 1; 11, 1; 13, 1; 53, 1; 1439, 1; 23561, 1; 413407351547, 1; 6700904941889, 1; 188122098214963717375891, 1]	10650
200	-75	[2, 2; 3, 2; 5, 2; 1973, 1; 4229, 1; 43481, 1; 4921441524559637294985132128164617176671474541, 1]	40
201	-55	[2, 3; 3, 1; 167, 1; 373, 1; 524970661658113207, 1; 4095034364012227742853788935311573767, 1]	34580
202	-183	[2, 3; 3, 1; 5, 1; 7, 1; 157, 1; 575359, 1; 132419253469, 1; 639720310844023611351180529144690508359, 1]	16320
203	-159	[2, 5; 159713901631, 1; 2515338408004754911311634508555703462104415468869, 1]	3150
204	-167	[2, 3; 701, 1; 2003, 1; 64203236540867, 1; 35651125041115722402818055390497311586431, 1]	49480
205	-81	[2, 1; 5, 2; 23, 1; 43, 1; 83, 1; 253733, 1; 5427671, 1; 9097336384850252124159720263087428101924419, 1]	60
206	-5	[2, 1; 1126397, 1; 8508294359, 1; 5365560786350470324266798915301651129633890023, 1]	380
207	-91	[2, 2; 3, 1; 7, 2; 1351359109, 1; 6447420331263374581, 1; 40149026429055639173984371262843, 1]	17370
208	-299	[2, 2; 11, 1; 179, 1; 930911, 1; 1331471, 1; 42139901560804743856900479669932824375331056501, 1]	80
209	-33	[2, 1; 19, 1; 223, 1; 1889, 1; 3557, 1; 10651, 1; 19163, 1; 1078853, 1; 79448717, 1; 825965228710894362828097778503, 1]	140
210	-47	[2, 4; 23, 1; 37, 1; 112921, 1; 369947, 1; 14056417, 1; 90762222332731247, 1; 2267543189131075664701547, 1]	1550
211	-175	[2, 4; 3, 1; 83472648601, 1; 39007069683614531, 1; 21057185723372201121181744082314069, 1]	28240
212	-23	[2, 3; 8792772968923, 1; 93571422982092467654057736798598978841081010309383, 1]	6050
213	-3	[2, 2; 15193, 1; 60272956433838849161, 1; 3593875704495823757388199894268773153439, 1]	191460
214	-185	[2, 1; 317, 1; 124058292389, 1; 540945037908779672551583, 1; 618800810497636303055388781, 1]	21950
215	-157	[2, 1; 3, 2; 5, 1; 7, 1; 5641, 1; 23997473, 1; 254926367, 1; 16758582209, 1; 144522303784397092260567539423893, 1]	830
216	-377	[2, 1; 13, 1; 32633, 1; 9982313543, 1; 206640513120169967, 1; 60173051501702045425514341939471, 1]	13820
217	-61	[2, 1; 3, 1; 5, 1; 11, 1; 2260519, 1; 3423826184329638478080176899, 1; 82466060547863089674548055737, 1]	85110
218	-33	[2, 1; 3, 1; 5, 1; 29, 1; 1487, 1; 325618321757321109996731914704977026393943202469058619157019, 1]	60
219	-121	[2, 1; 3, 1; 19, 1; 7331538732970798685879, 1; 1008019806839100702034857699988907432049661, 1]	761620
220	-77	[2, 1; 11, 1; 29, 1; 43, 1; 10729, 1; 5724672764986045690693560266306755552932768319387558211693, 1]	60
221	-3	[2, 2; 7, 1; 439, 1; 3943, 1; 2298041, 1; 9361973132609, 1; 671165898617413417, 1; 4815314615204347717321, 1]	24520
222	-117	[2, 1; 3, 3; 1010536301839123457339, 1; 123513195593586463868249598285337146648031981, 1]	1463770
223	-235	[2, 2; 3, 3; 1010536301839123457339, 1; 123513195593586463868249598285337146648031981, 1]	1487840
224	-63	[2, 6; 3, 1; 104124649, 1; 745988807, 1; 870035986098720987332873, 1; 2077756847362348863128179, 1]	9440
225	-49	[2, 1; 3, 1; 7, 1; 61, 1; 27943, 1; 162601, 1; 5940989, 1; 892101237234038665147, 1; 873978534303771245583941719, 1]	11440
226	-5	[2, 1; 53, 1; 47977, 1; 5979468433, 1; 36078102492307, 1; 98295537368972223482915638371315396139, 1]	4620
227	-405	[2, 1; 107839786668602559178668060348078522694548577690162289924414440996661, 1]	150
228	-93	[2, 1; 3, 1; 31237, 1; 626571587, 1; 404467716453060805507, 1; 9081631654249145670564546290497319, 1]	59960
229	-91	[2, 2; 3, 5; 5, 1; 40591, 1; 3143029, 1; 53627527, 1; 2004564824464229, 1; 12943350847025909190036177872551, 1]	8310
230	-27	[2, 2; 3, 1; 1373, 1; 5059, 1; 306329, 1; 52830590848430789043986747, 1; 1279113136179487092679920251063, 1]	53980
231	-165	[2, 1; 1427957, 1; 39658511108291893, 1; 30468246982477978515515525373918516398562133141, 1]	14160
232	-567	[2, 3; 3, 1; 47, 1; 427617987367, 1; 2044992909707736481033, 1; 6996842897906086565920734288250691, 1]	86940
233	-3	[2, 2; 7, 2; 23, 1; 89, 1; 127, 1; 337, 1; 463, 1; 599479, 1; 581283643249112959, 1; 4982397651178256151338302204762057, 1]	20110
234	-83	[2, 2; 5, 2; 816769, 1; 442138142271041, 1; 764472306154269432915984448077034681182685606499, 1]	18780
235	-15	[2, 4; 7, 2; 23, 1; 89, 1; 127, 1; 337, 1; 463, 1; 599479, 1; 581283643249112959, 1; 4982397651178256151338302204762057, 1]	20130
236	-209	[2, 1; 29, 1; 89, 1; 13544143745826932025021989329, 1; 1579462874256119876465031118434123019787, 1]	1737680
237	-181	[2, 1; 3, 1; 5, 1; 97, 1; 75895492473298295944299720822290314253757899350327274833402328234219, 1]	100
238	-161	[2, 1; 47, 1; 73, 1; 56346729743, 1; 23956921622110153, 1; 47685740029545205332343007648346758976959, 1]	121680
239	-87	[2, 3; 5, 2; 7, 1; 43, 1; 73186307755556536589, 1; 200513046199026997866779165419871806377600800341, 1]	755220
240	-467	[2, 2; 2207, 1; 388351518883, 1; 1573683962309, 1; 327487032512072551393739125381363838638459963, 1]	13090
241	-39	[2, 3; 59, 1; 71, 1; 125948811448546516414213434444739, 1; 837210244930902750478699457171126909, 1]	1981920
242	-63	[2, 6; 3, 1; 5, 1; 1181, 1; 2833, 1; 3541, 1; 37171, 1; 157649, 1; 174877, 1; 179951, 1; 5521693, 1; 1824726041, 1; 104399276341, 1; 3203431780337, 1]	510
243	-9	[2, 1; 1059474334145137324096576187719, 1; 6670655466907588375704838543306822887023021, 1]	15392250
244	-189	[2, 1; 3, 1; 197, 1; 11393, 1; 57847, 1; 51954001027703, 1; 253585377306339492449179, 1; 2754478086488356140570509, 1]	20050
245	-163	[2, 2; 3, 1; 11, 2; 10158033271, 1; 2651913793989357523, 1; 1445483997329846220738961002758581843746673, 1]	314370
246	-107	[2, 2; 11, 1; 23, 1; 9382223, 1; 208018359877, 1; 57252044712790847451834254170647452144376636229403003, 1]	9950
247	-81	[2, 1; 43, 1; 59, 1; 19219, 1; 23063, 1; 42043, 1; 5317979, 1; 148238165219161, 1; 3033971756400556566256483326377811571, 1]	23330
248	-237	[2, 1; 3, 3; 2117141551592677249, 1; 1634569665398669094989107, 1; 2420426137301208737721039667369, 1]	76900
249	-75	[2, 2; 265561467247, 1; 851616112217379844753490755648602262694659613077443581863618147, 1]	15710
250	-207	[2, 4; 3, 1; 17, 1; 2217219845996403864575118432304838921822724890196855163132996017308385601, 1]	110
251	-9	[2, 1; 19, 1; 3121, 1; 30510656070643106182115999270826633842178510774222732476374386585332681, 1]	60
252	-129	[2, 1; 3, 1; 43, 1; 41953, 1; 4979420713, 1; 12036730438063937, 1; 34400489300742979, 1; 324283015810421005973242541, 1]	140700
253	-273	[2, 1; 3187, 1; 913180633, 1; 696298366925826656521, 1; 3571287181702555779736074641734730653395149, 1]	433400
254	-245	[2, 1; 79, 1; 3539, 1; 701731, 1; 974497, 1; 75705961582336032110452308695156564214088210230278680011907, 1]	130
255	-19	[2, 2; 3, 1; 65147, 1; 74058212732561358302231226437062788676166966415465897661863160754340907, 1]	60
256	-189	[2, 1; 3, 1; 29, 1; 222587, 1; 1521613, 1; 4463413, 1; 440208639276132997491800604758226661590679912188273141493, 1]	170
257	-93	[2, 1; 9340679, 1; 81341356685870606963191, 1; 152401426061351045623332230958307016527107478801, 1]	2073100
258	-87	[2, 3; 3, 1; 61, 1; 10293527, 1; 30735026829701555603368594197526649635100056671893194944473989691077, 1]	100
259	-361	[2, 1; 3, 2; 13, 1; 3958703905549271638412683248160270353957948193697113300494276376338910415039, 1]	170
260	-149	[2, 1; 39677838514980433, 1; 124254106796695169449, 1; 187892791897923671034965331643020450024989, 1]	391020
261	-223	[2, 5; 3, 2; 1213, 1; 10606585072576366714625903179324714468560042563491853443203955666200708037, 1]	130
262	-71	[2, 3; 7, 1; 132333816271218509055509697152786180403737125332160644616522953151900719588497, 1]	80
263	-747	[2, 2; 5, 1; 13, 1; 23, 1; 2529295193, 1; 3186807992298761219, 1; 307490894123975068695172205186684212362429372841, 1]	8140
264	-275	[2, 2; 5, 1; 48142021, 1; 8014734557, 1; 351834291989734327369, 1; 10917852734093742584596187716460542066519, 1]	300430
265	-49	[2, 1; 3, 1; 211, 1; 569, 1; 14401, 1; 61519, 1; 4095144101, 1; 180005696950598015171, 1; 126021754756267282721431236694402967, 1]	60410
266	-3	[2, 2; 3, 2; 5, 1; 7, 1; 13, 1; 17, 1; 23, 1; 67, 1; 89, 1; 241, 1; 353, 1; 397, 1; 683, 1; 2113, 1; 7393, 1; 20857, 1; 312709, 1; 599479, 1; 4327489, 1; 1761345169, 1; 2931542417, 1; 98618273953, 1]	300
267	-265	[2, 1; 3, 1; 1285279, 1; 30751066338906905067236163937660336171303004846318954244280701187343511863, 1]	150
268	-77	[2, 1; 853, 1; 4007, 1; 6998239166167, 1; 1685101657977964436098042916777, 1; 5883362151411780955219936413101, 1]	204950
269	-241	[2, 1; 3, 1; 5, 1; 7, 2; 79, 1; 2897, 1; 36070621, 1; 192835543, 1; 10070723387194654603958653, 1; 40250802230324898226095552713353, 1]	81910
270	-53	[2, 1; 5, 1; 245264233171428526706685759014508458783, 1; 773507643382382537940525445158357764634239, 1]	75888120
271	-169	[2, 1; 3, 1; 7, 1; 202962937, 1; 2185050859, 1; 203704792088832476693249566666783482639927151412207570223511973, 1]	1050
272	-237	[2, 1; 3, 2; 47, 1; 1213, 1; 213181, 1; 19228060908107, 1; 1804029655689525238778676850714730275291908477571365155813, 1]	13320
273	-205	[2, 1; 3, 2; 11, 1; 17, 1; 17175751, 1; 104638110402919681507, 1; 2508817560202076618330089426158127322883090836024503, 1]	125580
274	-305	[2, 1; 3461, 1; 363169397, 1; 1330216529599, 1; 48129287350697028587, 1; 188601959565003541591329310209313129459, 1]	114840
275	-129	[2, 1; 7, 1; 1171, 1; 57119, 1; 81023, 1; 121012487, 1; 23126572387998467, 1; 285912738310404055442558568140607061991977799, 1]	14220
276	-89	[2, 1; 93151, 1; 15424926104694984601832839, 1; 42251116898694971565898093095827558920898935636831307, 1]	27730220
277	-103	[2, 3; 3, 1; 4921643, 1; 1192043179595340983, 1; 1724628115307254008646926255474975700090285775089771612453, 1]	279650
278	-93	[2, 1; 3, 4; 5, 2; 35845756259, 1; 1020823525559, 1; 142969853587413697146749, 1; 22921914141647811312957090726603001, 1]	103830
279	-69	[2, 1; 1091, 1; 18941102166895071951474817120841, 1; 23502215132880195699760075340804878804639464756839, 1]	929930
280	-47	[2, 4; 2267, 1; 15794983571, 1; 7172895177104937152863597, 1; 472730496784237941410822264147481185833429777, 1]	1611470
281	-139	[2, 2; 3, 2; 5490011, 1; 143729353, 1; 562853636631138634964038847, 1; 243003270776073371049230173446170609911817, 1]	1077950
282	-83	[2, 2; 5, 1; 983, 1; 196601219, 1; 141939161168963956627, 1; 14164029517496545688104807449480969946608408362803889, 1]	196730
283	-45	[2, 1; 886801991827, 1; 28989724280495264772289, 1; 302265118624242077340553796531431025151515415126227, 1]	11281030
284	-173	[2, 1; 457, 1; 3074677, 1; 2664231423869737, 1; 282340299704142310324867201811, 1; 14703754939989480218346599059927, 1]	287540
285	-9	[2, 1; 11, 1; 12964024748501, 1; 217964734076932156111514568114904890024605669950045660233263463447244301, 1]	30180
286	-165	[2, 1; 3, 1; 13, 1; 17, 1; 59, 1; 13395601, 1; 17357077, 1; 6835093044285482403773059278573741467423440621375941396611526528461, 1]	410
287	-115	[2, 2; 3, 1; 7, 2; 623947, 1; 91145996311, 1; 7436115590292125746476231065146276500165929614318792669020552211397, 1]	4160
288	-167	[2, 3; 11, 1; 30915205271, 1; 195588395871442085084354141883375067, 1; 934632459328397434628283569822381681093, 1]	7637820
289	-493	[2, 1; 3, 1; 83, 1; 439, 1; 1663, 1; 2735789224587787135900106826927580222007840642103286271103142487714316816383113, 1]	260
290	-47	[2, 4; 179, 1; 239, 1; 55487, 1; 85210324931, 1; 1965027863636852423, 1; 312806413638366750800158403702068227763702463651, 1]	1033260
291	-19	[2, 2; 3, 1; 585348671, 1; 566412534441700466029169189141082990631699524603912206758860112958964358313239, 1]	650
292	-167	[2, 3; 19, 2; 5737779741503, 1; 493552660435552898930183770513, 1; 972935779863472462574038604741160792087229, 1]	6585870
293	-601	[2, 1; 3, 1; 5, 1; 11, 1; 19, 1; 313, 1; 613, 1; 1779459827673225293, 1; 20885553271567040505321151, 1; 355944432370928964769077766990274891, 1]	321850
294	-35	[2, 2; 7, 1; 181, 1; 2243, 1; 160117, 1; 344954433409, 1; 115289130136570835298221037503, 1; 439708952144660222372920943482895053, 1]	705580
295	-171	[2, 2; 29, 1; 281, 1; 2659, 1; 3923, 1; 192111793130234469727, 1; 974526696113978976231067895091423651990398630487821207159, 1]	241700
296	-285	[2, 1; 3, 1; 5, 2; 29, 1; 61, 1; 44686146935516329, 1; 112855644192873231433667012161, 1; 95140062250539485941555268720020375427, 1]	1363510
297	-123	[2, 2; 97, 1; 226539943991, 1; 889210334327413690555212288427, 1; 3257824585446778203730453804073522631754188053, 1]	14728090
298	-341	[2, 1; 254629497041810760783555711051172270131433549208242031329517556169297662470417088272924501, 1]	240
299	-69	[2, 1; 7236263729652930604873, 1; 70375958244413911490548060385575964981946839433155608010982460524533, 1]	8197830
300	-153	[2, 1; 3, 4; 73, 1; 34267, 1; 3930559, 1; 34611060765077437061484737160485718539, 1; 36950090843062825976378737529596481741, 1]	7633740
301	-265	[2, 1; 3, 1; 11, 1; 173, 1; 197, 1; 653, 1; 1399, 1; 4957, 1; 399965576937104166381732366243036359049354126779234239327680973473089061829, 1]	190
302	-267	[2, 2; 3, 1; 11, 1; 17, 1; 2071645309265520077, 1; 406212279849849780121, 1; 4314866753718196817431654642039004568780931874857, 1]	1267630

ECC factorizations

Let the minus-one-factorization of a prime P be the factorization of P-1. Below are the minus-one-factorizations of the prime moduli for the Certicom Elliptic Curve Cryptography (ECC) Challenges over prime fields, and the recursive minus-one-factorizations of each large prime factor. If a number is followed by a parenthesized expression, the parenthesized expression, ignoring any parenthesized expressions within it, is the minus-one-factorization of the number.

;; ECCp-131
1550031797834347859248576414813139942411 ( 2 5 155003179783434785924857641481313994241 ( 2 2 2 2 2 2 2 2 2 3 5 20182705700968071083965838734546093 ( 2 2 3 3 13 23 31 691 1063 35425647529 (2 2 2 3 1476068647 (2 3 13 13 211 6899)) 2324421561859 ( 2 3 11 5591 6299143 (2 3 1049857 (2 2 2 2 2 2 2 2 3 1367))))))

;; ECCp-163
7441570001851253078325059510076520610606604922267 (2 3 19 281082065814119 (2 4021 34951761479 (2 9341 1870879 (2 3 79 3947))) 232234417559633389665439706088451 (2 3 5 5 199 601 1517753 (2 2 2 193 983) 42683677 (2 2 3 7 23 22093) 199822713017 (2 2 2 13709 1822003 (2 3 7 13 47 71) )))

;; ECCp-191
3088527565889291933677698411347346523477823907719021786597 (2 2 7 64817 176597 2831642591 (2 5 7 71 569747) 612429643268111 (2 5 61 3533 10831 26237) 5556822995668202328643 (2 3 11 13 13 37 13464623031049829 (2 2 11 11 11 17 181 821918311 (2 3 5 27397277 (2 2 1979 3461)))))

;; ECCp-239
862591559561497151050143615844796924047865589835498401307522524859467869 (2 2 79 97 683 32914695791553889 (2 2 2 2 2 3 13 26373954961181 (2 2 5 6481 11681 17419)) 1251802568002522287870807195430320302070461232107 (2 83 7949 17337811 (2 3 5 7 82561) 1865415619 (2 3 3 11 11 47 18223) 14584787891 (2 5 1458478789 (2 2 3 13 13 29 24799)) 2011153700906761 (2 2 2 3 5 16759614174223 (2 3 19 63607 2311289 (2 2 2 7 149 277)))) )

;; ECCp-359
815061317237192195822186322581994619328922585201839923945006339195983201432548797517008668016697623370770793 ( 2 2 2 59 18761087 (2 29 323467) 32129831 (2 5 17 188999) 2864717788343148103646536857871784899879148861068940844995306009883386685231752208772094863 ( 2 3 127 265921867653623936056279 ( 2 3 3 14773437091867996447571 (2 5 7 17 2477987 (2 7 263 673) 5009975039569 (2 2 2 2 3 104374479991 (2 3 5 11 3797 83299))) ) 14137506615578070034728506896758540845078851196564075028357231269 ( 2 2 19 67 67 5414567 (2 2707283 (2 1353641 (2 2 2 5 43 787))) 677259217957139 (2 127 389 8951 765773) 1246739038251570197 (2 2 113 733 3762990734681 (2 2 2 5 226463 415409)) 9063906319214216867 (2 11 823 6301 79448081161 (2 2 2 3 5 7 61 1550509 (2 2 3 129209))))))

The most difficult factorization was 283..863 in ECCp-359, after dividing by 762 has a large composite 3759472163179984387987581178309429002466074620825381686345545944728853917626971402588051.