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

13, 2481757, 13703077, 15546404183, 2549536629329

Offset: 1

Author

Alexander Adamchuk, Mar 26 2007

Keywords

• hard
• more
• nonn

Comments

No further terms up to 3.127*10^13.

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)

Crossrefs

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

Programs

Mathematica

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