A236173 Primes p such that p^2 - p - 1, p^3 - p - 1 and p^4 - p - 1 are all prime.

11, 71, 11621, 28151, 32089, 37501, 39209, 45329, 66161, 76649, 114599, 122131, 136949, 154991, 202999, 228901, 243391, 270269, 296911, 313909, 318679, 333701, 343309, 359291, 369979, 371281, 371981, 373171, 373459

Offset: 1

Author

Derek Orr, Jan 19 2014

Keywords

• nonn

Comments

Primes in A236171. All primes appear to end in a 1 or a 9 (congruent to either 1 mod 10 or 9 mod 10).

Examples

			228901 is prime, 228901^2 - 228901 - 1 is prime, 228901^3 - 228901 - 1 is prime, and 228901^4 - 228901 - 1 is prime. So 228901 is a member of this sequence.
		

Links

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

Crossrefs

Cf. A091567, A236168, A236071.

Programs

Mathematica

Select[Prime[Range[32000]],AllTrue[#^{2,3,4}-#-1,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 08 2019 *)

PARI

s=[]; forprime(p=2, 400000, if(isprime(p^2-p-1) && isprime(p^3-p-1) && isprime(p^4-p-1), s=concat(s, p))); s \\ Colin Barker, Jan 20 2014

Python

import sympy
from sympy import isprime
{print(p) for p in range(10**6) if isprime(p) and isprime(p**2-p-1) and isprime(p**3-p-1) and isprime(p**4-p-1)}