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

2, 7, 31, 859

Offset

1,1

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

Links

Table of n, a(n) for n=1..4.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A090669.

Sequence in context: A309164 A102163 A102164 * A102165 A102160 A215434

Adjacent sequences: A147779 A147780 A147781 * A147783 A147784 A147785

Keyword

nonn,hard,more

Author

Cino Hilliard, Nov 12 2008

Extensions

Offset corrected by Mohammed Yaseen, Jul 20 2023

Status

approved