A236940 Primes p such that p^4-p+1 is prime.

3, 13, 19, 43, 79, 109, 313, 379, 613, 709, 1171, 1213, 1399, 1543, 1693, 1759, 1861, 1933, 2089, 2239, 2341, 2371, 2503, 2521, 2731, 2749, 3001, 3061, 3229, 3433, 3571, 3739, 3769, 4219, 4801, 4933, 4951, 4993, 5011, 5023, 5209, 5281

Offset: 1

Author

Derek Orr, Feb 01 2014

Keywords

• nonn

Comments

Primes in the sequence A236761.

Examples

			1213 is prime and 1213^4 - 1213 + 1 = 2164926732949 is prime. Thus, 1213 is a member of this sequence.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A236761.

Programs

Magma

[p: p in PrimesUpTo(6000) | IsPrime(p^4-p+1)]; // Vincenzo Librandi, Feb 14 2014

Mathematica

Select[Prime[Range[10000]], PrimeQ[#^4 - # + 1]&] (* Vincenzo Librandi, Feb 14 2014 *)

PARI

s=[]; forprime(p=2, 6000, if(isprime(p^4-p+1), s=concat(s, p))); s \\ Colin Barker, Feb 05 2014

Python

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