A378702 Primes p such that 256*p^8 + 1 is prime.

2, 59, 271, 281, 433, 467, 587, 971, 1039, 1097, 1181, 1277, 1283, 1361, 1373, 1427, 1447, 1481, 1579, 1657, 1777, 2089, 2129, 2269, 2381, 2617, 2753, 2803, 2939, 3181, 3319, 3691, 3823, 4093, 4217, 4241, 4327, 4909, 4999, 5279, 5303, 5387, 5483, 6043, 6121, 6197, 6221, 6563, 6577, 7159, 7243, 7867

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 04 2024

Keywords

• nonn

Crossrefs

Primes p such that (2*p)^(2^n) + 1 is prime: A005384 (n = 0), A052291 (n = 1), A378146 (n = 2), this sequence (n = 3).

Cf. A006314, A378134, A378143.

Programs

Magma

[p: p in PrimesUpTo(8000) | IsPrime(256*p^8 + 1)];

Mathematica

Select[Prime[Range[1000]], PrimeQ[(2*#)^8 + 1] &] (* Amiram Eldar, Dec 06 2024 *)

PARI

select(p->isprime(256*p^8+1), primes(10^6)) \\ Charles R Greathouse IV, Dec 04 2024

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Dec 04 2024