A123693 Primes p such that p^2 divides 7^(p-1) - 1.

5, 491531

Offset: 1

Author

Max Alekseyev, Oct 07 2006

Keywords

• bref
• hard
• nonn
• more

Comments

Dorais and Klyve proved that there are no further terms up to 9.7*10^14.

Links

• Amir Akbary and Sahar Siavashi, The Largest Known Wieferich Numbers, INTEGERS, 18(2018), A3. See Table 1 p. 5.
• F. G. Dorais and D. Klyve, A Wieferich prime search up to p < 6.7*10^15, J. Integer Seq. 14 (2011), Art. 11.9.2, 1-14.
• W. Keller and J. Richstein, Fermat quotients q_p(a) that are divisible by p.

Crossrefs

Cf. A001220, A014127, A123692, A123693, A128667, A128668, A090968, A039951, A128669

Programs

Mathematica

Select[Prime[Range[1000000]], PowerMod[7, # - 1, #^2] == 1 &] (* Robert Price, May 17 2019 *)

Extensions

Updated by Max Alekseyev, Jan 29 2012