A237641 Primes p of the form n^2-n-1 (for prime n) such that p^2-p-1 is also prime.

5, 236681, 380071, 457651, 563249, 1441199, 1660231, 2491661, 3050261, 4106701, 5137021, 5146091, 5329171, 10617821, 15574861, 19860391, 20852921, 21349019, 21497131, 23025601, 24507449, 32495699, 36342811, 48867089, 51129649, 59082281

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.

These are the primes in the sequence A237527.

Examples

			5 = 3^2-3^1-1 (3 is prime) and 5^2-5-1 = 19 is prime. Since 5 is prime too, 5 is a member of this sequence.
		

Crossrefs

Cf. A237527, A091567, A091568.

Programs

Mathematica

Select[Table[n^2-n-1,{n,Prime[Range[1000]]}],AllTrue[{#,#^2-#-1},PrimeQ]&] (* Harvey P. Dale, Aug 14 2024 *)

PARI

s=[]; forprime(n=2, 40000, 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
def poly2(x):
  if isprime(x):
    f = x**2-x-1
    if isprime(f**2-f-1):
      return True
  return False
x = 1
while x < 10**5:
  if poly2(x):
    if isprime(x**2-x-1):
      print(x**2-x-1)
  x += 1