A147782 Primes p such that 7^p - 2 is prime.

2, 7, 31, 859

Offset: 1

Author

Cino Hilliard, Nov 12 2008

Keywords

• nonn
• hard
• more

Comments

m=7 in the PARI script. 13 is the next base prime for which this condition holds. In fact, the base prime q in q^p-2 is prime must be of the form 6n+1.

This follows from the fact that if q = 6n-1, the binomial q^p = (6n-1)^p = 6h-1 for some h and q^p-2 = 6h-1-2 is divisible by 3 and thus not prime.

a(5) > 90263. - J.W.L. (Jan) Eerland, Dec 11 2022

a(5) > 274120 using A090669. - Michael S. Branicky, Jul 07 2024

Crossrefs

Cf. A000040, A090669.

Programs

Mathematica

Select[Prime[Range[150]],PrimeQ[7^#-2]&] (* Harvey P. Dale, Feb 20 2013 *)

PARI

g(n,m)=forprime(p=2,n,y=m^p-2;if(ispseudoprime(y),print1(p",")))

Formula

A000040 INTERSECT A090669. - R. J. Mathar, Jan 22 2009

Extensions

Offset corrected by Mohammed Yaseen, Jul 20 2023