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 A212583 Primes p such that p^2 divides 6^(p-1) - 1. 12
 66161, 534851, 3152573 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Base 6 Wieferich primes. Next term > 4.119*10^13. [See Fischer link] REFERENCES P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1996, page 347 LINKS Table of n, a(n) for n=1..3. Amir Akbary and Sahar Siavashi, The Largest Known Wieferich Numbers, INTEGERS, 18(2018), A3. See Table p. 5. François G. Dorais and Dominic Klyve, A Wieferich prime search up to p < 6.7*10^15, J. Integer Seq. 14 (2011), Art. 11.9.2, 1-14. Richard Fischer, Thema: Fermatquotient B^P-1 == 1 mod (P^2) Wilfrid Keller and Jörg Richstein, Fermat quotients q_p(a) that are divisible by p. Eric Weisstein, Fermat Quotient, MathWorld Wikipedia, Base-a Wieferich primes MATHEMATICA Select[Prime[Range[1000000]], PowerMod[6, # - 1, #^2] == 1 &] (* Robert Price, May 17 2019 *) PROG (PARI) N=10^9; default(primelimit, N); forprime(n=2, N, if(Mod(6, n^2)^(n-1)==1, print1(n, ", "))); \\ Joerg Arndt, May 01 2013 CROSSREFS Cf. A001220, A014127, A090968, A123692, A123693, A128667, A128668, A128669. Sequence in context: A254185 A253797 A241978 * A156424 A092376 A251333 Adjacent sequences: A212580 A212581 A212582 * A212584 A212585 A212586 KEYWORD nonn,hard,bref,more AUTHOR Felix Fröhlich, May 22 2012 STATUS approved

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Last modified July 25 15:49 EDT 2024. Contains 374612 sequences. (Running on oeis4.)