A236073 Primes p such that p^4 + p + 1 and p^4 - p - 1 are also prime.

2, 5, 11, 239, 1871, 4001, 4397, 6971, 12647, 12689, 13337, 13619, 15401, 19391, 19559, 19739, 20201, 20297, 22871, 22937, 28307, 30029, 32561, 36299, 36929, 39569, 44279, 45497, 47441, 48767, 50069, 53897, 55871

Offset: 1

Author

Derek Orr, Jan 19 2014

Keywords

• nonn

Comments

Primes in the sequence A236072.

Examples

			6971 is prime, 6971^4 - 6971 - 1 is prime, and 6971^4 + 6971 + 1 is prime. So 6971 is a member of this sequence.
		

Crossrefs

Cf. A236072, A236071, A236044.

Programs

PARI

s=[]; forprime(p=2, 55871, if(isprime(p^4+p+1)&&isprime(p^4-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 19 2014

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**5) if isprime(p**4+p+1) and isprime(p**4-p-1) and isprime(p)}