A128669 Primes p such that p^2 divides 23^(p-1) - 1.

13, 2481757, 13703077, 15546404183, 2549536629329

Offset

1,1

Comments

No further terms up to 3.127*10^13.

Primes p such that binomial(23*p^2,p^2) == 23^p mod p^2. - Chai Wah Wu, Jun 26 2026

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).

Mathematica

Select[Prime[Range[5*10^7]], Mod[ 23^(# - 1) - 1, #^2] == 0 &] (* G. C. Greubel, Jan 18 2018 *)
(* Alternative: *)
Select[Prime[Range[93*10^9]], PowerMod[23, #-1, #^2]==1&] (* Harvey P. Dale, May 15 2018 *)

Crossrefs

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

Sequence in context: A055324 A228538 A055313 * A013866 A014384 A185213

Adjacent sequences: A128666 A128667 A128668 * A128670 A128671 A128672

Keyword

nonn,hard,more,changed

Author

Alexander Adamchuk, Mar 26 2007

Status

approved