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%I #22 Apr 27 2019 05:43:06
%S 13,673,1595813,492366587,9809862296159
%N Wieferich primes to base 22.
%C Prime numbers p such that p^2 divides 22^(p-1) - 1.
%C Next term, if it exists, is larger than 8.72*10^13.
%C 492366587 was found by Montgomery (cf. Montgomery, 1993). - _Felix Fröhlich_, Jan 30 2018
%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 1 p. 5.
%H Richard Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/">Fermatquotient B^(P-1) == 1 (mod P^2)</a>
%H P. L. Montgomery, <a href="http://www.jstor.org/stable/2152960">New Solutions of a^p-1 == 1 (mod p^2)</a>, Mathematics of Computation, Vol. 61, No. 203 (1993), 361-363.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wieferich_prime">Wieferich prime</a>
%o (PARI) forprime(p=1, , if(Mod(22, p^2)^(p-1)==1, print1(p, ", ")))
%Y Wieferich primes to base b: A001220 (b=2), A014127 (b=3), A123692 (b=5), A212583 (b=6), A123693 (b=7), A045616 (b=10), A111027 (b=12), A128667 (b=13), A234810 (b=14), A242741 (b=15), A128668 (b=17), A244260 (b=18), A090968 (b=19), A242982 (b=20), this sequence (b=22), A128669 (b=23), A306255 (b=26), A306256 (b=30).
%K nonn,more,hard
%O 1,1
%A _Tim Johannes Ohrtmann_, Jan 30 2018
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