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%I #37 May 17 2019 14:42:59
%S 66161,534851,3152573
%N Primes p such that p^2 divides 6^(p-1) - 1.
%C Base 6 Wieferich primes.
%C Next term > 4.119*10^13. [See Fischer link]
%D P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, 1996, page 347
%H Amir Akbary and Sahar Siavashi, <a href="http://math.colgate.edu/~integers/s3/s3.Abstract.html">The Largest Known Wieferich Numbers</a>, INTEGERS, 18(2018), A3. See Table p. 5.
%H François G. Dorais and Dominic Klyve, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Klyve/klyve3.html">A Wieferich prime search up to p < 6.7*10^15</a>, J. Integer Seq. 14 (2011), Art. 11.9.2, 1-14.
%H Richard Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort">Thema: Fermatquotient B^P-1 == 1 mod (P^2)</a>
%H Wilfrid Keller and Jörg Richstein, <a href="http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients q_p(a) that are divisible by p</a>.
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/FermatQuotient.html">Fermat Quotient</a>, MathWorld
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Wieferich_prime#Base-a_Wieferich_primes">Base-a Wieferich primes</a>
%t Select[Prime[Range[1000000]], PowerMod[6, # - 1, #^2] == 1 &] (* _Robert Price_, May 17 2019 *)
%o (PARI)
%o N=10^9; default(primelimit,N);
%o forprime(n=2,N,if(Mod(6,n^2)^(n-1)==1,print1(n,", ")));
%o \\ _Joerg Arndt_, May 01 2013
%Y Cf. A001220, A014127, A090968, A123692, A123693, A128667, A128668, A128669.
%K nonn,hard,bref,more
%O 1,1
%A _Felix Fröhlich_, May 22 2012
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