A128668 Primes p such that p^2 divides 17^(p-1) - 1.

2, 3, 46021, 48947, 478225523351

Offset: 1

Author

Alexander Adamchuk, Mar 26 2007

Keywords

• hard
• more
• nonn

Comments

Mossinghoff showed that there are no further terms up to 10^14.

References

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

Links

• Amir Akbary and Sahar Siavashi, The Largest Known Wieferich Numbers, INTEGERS, 18(2018), A3. See Table 1 p. 5.
• Richard Fischer, Fermat quotients B^(P-1) == 1 (mod P^2)
• M. J. Mossinghoff, Wieferich pairs and Barker sequences, Des. Codes Cryptogr. 53 (2009), 149-163.

Crossrefs

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

Programs

Mathematica

Select[Prime[Range[5*10^6]], Mod[ 17^(# - 1) - 1, #^2] == 0 &] (* G. C. Greubel, Jan 18 2018 *)

Extensions

The prime 478225523351 was found by Richard Fischer on Oct 25 2005

Extension corrected by Jonathan Sondow, Jun 24 2010