A344360 Primes p such that (2^p - 2)/p + 1 is prime.

2, 3, 5, 7, 13, 53, 67, 83, 167, 1367, 2473, 4789, 34127, 219217

Offset: 1

Author

Jorge Coveiro, May 15 2021

Keywords

• nonn
• more

Comments

a(15) > 1099997, if it exists. - Karl-Heinz Hofmann, Jul 27 2021

These are primes p such that 2^((2^p-2)/p) == 1 (mod (2^p-2)/p+1) if and only if there are no pseudoprimes of the form (2^q-2)/q+1 with q prime. - Thomas Ordowski, Aug 29 2021

Examples

			7 is a term because (2^7 - 2)/7 + 1 = 19 is prime.
		

Crossrefs

Cf. A064535, A344361.

Programs

Mathematica

Select[Prime@ Range[10^3], PrimeQ[(2^# - 2)/# + 1] &] (* Michael De Vlieger, Oct 12 2021 *)

PARI

lista(lim)={forprime(p=1,lim,if(ispseudoprime((2^p-2)/p+1), print1(p,", ")))}

PARI

c3(p) = {s=3; for(x=1, p, s=(s^2)%((2^p-2)/p+1)); if(s==9, print1(p, ", "))} /* PRP Test */

Extensions

a(14) from Karl-Heinz Hofmann, Jun 11 2021