A240084 Primes p such that p^4-p^3-p^2-p-1 is prime.

3, 11, 17, 41, 59, 71, 101, 113, 179, 233, 293, 347, 389, 449, 461, 503, 521, 617, 641, 683, 797, 953, 1319, 1439, 1487, 1493, 1823, 1877, 1973, 2087, 2339, 2351, 2633, 2663, 2789, 2801, 2909, 2927, 2957, 2963, 2999, 3011, 3167, 3467, 3527, 3677, 3851, 3881, 3923

Offset: 1

Author

Derek Orr, Mar 31 2014

Keywords

• nonn

Examples

			3^4-3^3-3^2-3-1 = 41 is prime. Thus, 3 is a member of this sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A173179.

Programs

Mathematica

Select[Prime[Range[600]],PrimeQ[#^4-#^3-#^2-#-1]&] (* Harvey P. Dale, Nov 23 2024 *)

PARI

s=[]; forprime(p=2, 4000, if(isprime(p^4-p^3-p^2-p-1), s=concat(s, p))); s \\ Colin Barker, Apr 01 2014

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p**4-p**3-p**2-p-1) and isprime(p)}