Monday, November 19, 2018

[ktngyprd] Primes one greater than small multiples of powers of 2

More precisely, the exponents are of the form e={1,3,5}*2^n.  The multiplier k is the smallest k such that P=k*2^e+1 is prime.

These are compactly expressible primes P for which P-1 is easy to factor.

1*2^0+1
1*2^1+1
1*2^2+1
5*2^3+1
1*2^4+1
3*2^5+1
3*2^6+1
1*2^8+1
13*2^10+1
3*2^12+1
1*2^16+1
7*2^20+1
45*2^24+1
43*2^32+1
27*2^40+1
15*2^48+1
25*2^64+1
195*2^80+1
57*2^96+1
21*2^128+1
141*2^160+1
133*2^192+1
207*2^256+1
7*2^320+1
553*2^384+1
223*2^512+1
141*2^640+1
63*2^768+1
1125*2^1024+1
25*2^1280+1
877*2^1536+1
2577*2^2048+1
1923*2^2560+1
4987*2^3072+1
3091*2^4096+1
2247*2^5120+1
11131*2^6144+1
9165*2^8192+1

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