A112634 Mersenne prime indices that are not Gaussian primes.

2, 5, 13, 17, 61, 89, 521, 2281, 3217, 4253, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 132049, 859433, 1398269, 2976221, 3021377, 6972593, 13466917, 30402457, 32582657, 42643801, 43112609, 57885161

Offset: 1

Author

Jorge Coveiro, Dec 27 2005

Keywords

• nonn
• more

Comments

57885161, 74207281 and 77232917 are in this sequence as well. - Ivan Panchenko, Apr 13 2018

82589933 is in the sequence as well. - David Benjamin, Mar 30 2022

136279841 is in the sequence. - David Benjamin, Nov 11 2024

Other than the term 2, primes p (A000043) such that 2^p - 1 is prime (A000668) and congruent to 31 mod 120. - Jianing Song, Nov 18 2024

Links

• Chris K. Caldwell, The largest known primes.

Crossrefs

Cf. A000043, A112633, A002313.

Programs

Mathematica

Select[MersennePrimeExponent[Range[48]], Mod[#, 4] != 3 &] (* Amiram Eldar, Oct 18 2024 *)

PARI

is(n)=n%4 < 3 && isprime(n) && isprime(2^n-1) \\ Charles R Greathouse IV, Nov 28 2016

Formula

A000043 INTERSECT A002313. - R. J. Mathar, Oct 06 2008

A000043 SET-MINUS A112633.

Extensions

Edited by R. J. Mathar, Oct 06 2008

a(26)-a(28) from Ivan Panchenko, Apr 13 2018

a(29) from Amiram Eldar, Oct 18 2024