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

2, 3, 46021, 48947, 478225523351

Offset

1,1

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

Table of n, a(n) for n=1..5.

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).

Michael J. Mossinghoff, Wieferich pairs and Barker sequences, Des. Codes Cryptogr. 53 (2009), 149-163.

Mathematica

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

Crossrefs

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

Sequence in context: A197635 A171161 A101445 * A216977 A331426 A300191

Adjacent sequences: A128665 A128666 A128667 * A128669 A128670 A128671

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Mar 26 2007

Extensions

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

Extension corrected by Jonathan Sondow, Jun 24 2010

Status

approved