A244260 Primes p such that p^2 divides 18^(p-1) - 1.

5, 7, 37, 331, 33923, 1284043

Offset: 1

Author

Felix Fröhlich, Jun 24 2014

Keywords

• nonn
• hard
• more

Comments

Base 18 Wieferich primes. According to Richard Fischer there is no other term up to approximately 5*10^13.

Links

• Amir Akbary and Sahar Siavashi, The Largest Known Wieferich Numbers, INTEGERS, 18(2018), A3. See Table 1 p. 5.
• R. Fischer, Thema: Fermatquotient B^(P-1) == 1 (mod P^2)

Crossrefs

Cf. A001220, A014127, A123692, A212583, A123693, A045616, A111027, A128667, A234810, A242741, A128668, A090968, A242982, A039951, A096082.

Programs

Mathematica

Select[Prime[Range[1000000]], PowerMod[18, # - 1, #^2] == 1 &] (* Robert Price, May 17 2019 *)

PARI

forprime(n=2, 10^9, if(Mod(18, n^2)^(n-1)==1, print1(n, ", ")));