A331424 Prime numbers p such that p^2 divides 31^(p-1) - 1.

7, 79, 6451, 2806861

Offset: 1

Author

Seiichi Manyama, Jan 16 2020

Keywords

• nonn
• more

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 233.

Links

• Richard Fischer, Fermatquotienten von 2 bis 1052, Dec 19 2019.
• Wikipedia, Wieferich prime

Crossrefs

Wieferich primes to base b: A001220 (b=2), A014127 (b=3), A123692 (b=5), A123693 (b=7), A128667 (b=13), A128668 (b=17), A090968 (b=19), A128669 (b=23), this sequence (b=31), A331426 (b=37), A331427 (b=41).

Cf. A039951.

Programs

Mathematica

Select[Range[3*10^6], PrimeQ[#] && PowerMod[31, # - 1, #^2] == 1 &] (* Amiram Eldar, May 05 2021 *)

PARI

forprime(p=2, 1e8, if(Mod(31, p^2)^(p-1)==1, print1(p", ")))