A355959 Primes p such that (p+2)^(p-1) == 1 (mod p^2).

5, 45827

Offset: 1

Author

Felix Fröhlich, Jul 21 2022

Keywords

• nonn
• hard
• more
• bref

Comments

a(3) > 107659373057 if it exists.

Primes p such that the Fermat quotient of p base 2 (A007663) is congruent to 1/2 modulo p. - Max Alekseyev, Aug 27 2023

Crossrefs

(p+k)^(p-1) == 1 (mod p^2): A355960 (k=5), A355961 (k=6), A355962 (k=7), A355963 (k=8), A355964 (k=9), A355965 (k=10).

Cf. A007663.

Programs

PARI

forprime(p=1, , if(Mod(p+2, p^2)^(p-1)==1, print1(p, ", ")))