A236478 Primes p such that p^3 - p + 1 is prime.

2, 7, 11, 19, 31, 41, 101, 139, 167, 239, 271, 277, 307, 347, 419, 449, 479, 491, 521, 547, 557, 587, 617, 619, 631, 647, 739, 757, 761, 769, 787, 809, 827, 839, 857, 971, 977, 991, 1019, 1069, 1187, 1201, 1217, 1231, 1277, 1487, 1621, 1637, 1709, 1747, 1861

Offset: 1

Author

Derek Orr, Jan 26 2014

Keywords

• nonn

Comments

Primes in the sequence A236477.

Examples

			419 is prime and 419^3 - 419 + 1 = 73559641 is prime. So 419 is a member of this sequence.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A236477.

Programs

Mathematica

Select[Prime[Range[300]],PrimeQ[#^3-#+1]&] (* Harvey P. Dale, Oct 30 2021 *)

PARI

s=[]; forprime(p=2, 2000, if(isprime(p^3-p+1), s=concat(s, p))); s \\ Colin Barker, Jan 27 2014

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n) and isprime(n**3-n+1)}

Extensions

More terms from Colin Barker, Jan 27 2014