A378146 Primes p such that 16*p^4 + 1 is prime.

2, 3, 17, 23, 37, 41, 53, 59, 71, 97, 127, 139, 167, 233, 263, 277, 283, 379, 389, 457, 521, 563, 571, 601, 619, 661, 691, 743, 797, 809, 811, 823, 853, 859, 877, 967, 971, 997, 1051, 1063, 1103, 1187, 1277, 1289, 1321, 1367, 1399, 1433, 1451, 1499

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 17 2024

Keywords

• nonn

Crossrefs

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

Cf. A378134, A378143.

Programs

Magma

[p: p in PrimesUpTo(1500) | IsPrime(16*p^4+1)];

Mathematica

Select[Prime[Range[250]], PrimeQ[16*#^4 + 1] &] (* Amiram Eldar, Nov 17 2024 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(16*p^4+1), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Nov 17 2024

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Nov 17 2024