

A122094


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


12



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS



FORMULA

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


MATHEMATICA

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


PROG

(PARI) forprime(p=3, 10^5, if(isprime(znorder(Mod(2, p))), print1(p, ", ")))
(Magma) [p: p in PrimesInInterval(2, 4000)  IsPrime(Modorder(2, p))]; // Vincenzo Librandi, Oct 28 2016


CROSSREFS

Cf. A089162 (this list sorted by q).


KEYWORD

nonn


AUTHOR



STATUS

approved



