A188130 Primes p such that 6p+1 divides the Mersenne number M(p)=A000225(p).

5, 37, 73, 233, 397, 461, 557, 577, 601, 761, 1013, 1321, 1361, 1381, 1453, 1693, 1777, 1993, 2417, 2593, 2621, 2897, 3037, 3181, 3457, 3581, 3593, 4001, 4273, 4441, 4517, 4597, 4801, 4813, 4861, 4933, 5197, 5393, 5557, 5717, 5801, 6173, 6277, 6353, 6373, 6841, 6977, 7573, 7853, 7901, 8353, 8377, 9613, 10321, 10357

Offset: 1

Author

M. F. Hasler, Mar 21 2011

Keywords

• nonn

Comments

These primes are such that p=1 (mod 4) and 6p+1 is prime, but there are other primes with these properties (13, 17, ...) not in this sequence.

There are no primes p such that 4p+1 divides M(p), but those for which 2p+1 divides M(p) are the Lucasian primes A002515, and those for which 10p+1 divides M(p) are listed in A188133.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1313 from M. F. Hasler)

Crossrefs

Cf. A002515, A188133.

Primes in A038844.

Programs

Mathematica

Select[Range[10^4], PrimeQ[#] && PowerMod[2, #, 6# + 1] == 1 &] (* Amiram Eldar, Nov 13 2019 *)

PARI

forprime(p=1,1e5,Mod(2,p*6+1)^p-1||print1(p", "))