A212583 Primes p such that p^2 divides 6^(p-1) - 1.

66161, 534851, 3152573

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