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A123693 Primes p such that p^2 divides 7^(p-1) - 1.

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%I A123693 #20 May 17 2019 14:42:51
%S A123693 5,491531
%N A123693 Primes p such that p^2 divides 7^(p-1) - 1.
%C A123693 Dorais and Klyve proved that there are no further terms up to 9.7*10^14.
%H A123693 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 1 p. 5.
%H A123693 F. G. Dorais and D. 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 A123693 W. Keller and J. Richstein, <a href="http://www1.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html">Fermat quotients q_p(a) that are divisible by p</a>.
%t A123693 Select[Prime[Range[1000000]], PowerMod[7, # - 1, #^2] == 1 &] (* _Robert Price_, May 17 2019 *)
%Y A123693 Cf. A001220, A014127, A123692, A123693, A128667, A128668, A090968, A039951, A128669
%K A123693 bref,hard,nonn,more
%O A123693 1,1
%A A123693 _Max Alekseyev_, Oct 07 2006
%E A123693 Updated by _Max Alekseyev_, Jan 29 2012