A237642 Primes of the form n^2-n-1 (for some n) such that p^2-p-1 is also prime.

5, 11, 29, 71, 131, 181, 379, 419, 599, 1979, 2069, 3191, 4159, 13339, 14519, 17291, 19739, 20879, 21169, 26731, 30449, 31151, 39799, 48619, 69959, 70489, 112559, 122849, 132859, 139501, 149381, 183611, 186191, 198469, 212981, 222311, 236681

Offset: 1

Author

Derek Orr, Feb 10 2014

Keywords

• nonn

Comments

Except a(1), all numbers are congruent to 1 mod 10 or 9 mod 10.

Examples

			11 is prime and equals 4^2-4-1, and 11^2-11-1 = 109 is prime. So, 11 is a member of this sequence.
		

Links

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

Crossrefs

Cf. A002327, A091568.

Programs

Mathematica

Select[Table[n^2-n-1,{n,500}],AllTrue[{#,#^2-#-1},PrimeQ]&] (* Harvey P. Dale, Feb 27 2023 *)

PARI

s=[]; for(n=1, 1000, p=n^2-n-1; if(isprime(p) && isprime(p^2-p-1), s=concat(s, p))); s \\ Colin Barker, Feb 11 2014

Python

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