A122094 Prime divisors of Mersenne numbers. Primes p such that the multiplicative order of 2 modulo p is prime.

3, 7, 23, 31, 47, 89, 127, 167, 223, 233, 263, 359, 383, 431, 439, 479, 503, 719, 839, 863, 887, 983, 1103, 1319, 1367, 1399, 1433, 1439, 1487, 1823, 1913, 2039, 2063, 2089, 2207, 2351, 2383, 2447, 2687, 2767, 2879, 2903, 2999, 3023, 3119, 3167, 3343

Offset: 1

Author

Max Alekseyev, Oct 25 2006

Keywords

• nonn

Comments

Except for the first term (3), all terms are 1 or 7 (mod 8). - William Hu, May 03 2024

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A001348, A016047, A003260, A000668, A137332.

Cf. A089162 (this list sorted by q).

Programs

Magma

[p: p in PrimesInInterval(2, 4000) | IsPrime(Modorder(2, p))]; // Vincenzo Librandi, Oct 28 2016

Mathematica

Reap[For[p=2, p<10^5, p=NextPrime[p], If[PrimeQ[MultiplicativeOrder[2, p]], Sow[p]]]][[2, 1]] (* Jean-François Alcover, Dec 10 2015 *)
Select[Prime@ Range@ 500, PrimeQ@ MultiplicativeOrder[2, #] &] (* Michael De Vlieger, Oct 28 2016 *)

PARI

forprime(p=3,10^5,if(isprime(znorder(Mod(2,p))),print1(p,",")))

Formula

p is a prime divisor of a Mersenne number 2^q - 1 iff prime q is the multiplicative order of 2 modulo p.