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%I #23 Jun 19 2021 20:10:41
%S 29,353,7596952219
%N Primes p such that p^2 divides 14^(p-1) - 1.
%C Base 14 Wieferich primes.
%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 Petr Ležák, <a href="http://download2.polytechnic.edu.na/pub4/sourceforge/w/wi/wieferich/results/table.txt">Solutions of equation a^(p-1) mod p^2 = 1, p is prime</a>
%H P. L. Montgomery, <a href="http://dx.doi.org/10.1090/S0025-5718-04-01666-7">New solutions of a^p-1 == 1 (mod p^2)</a>, Math. Comp., 61 (203), 361-363
%t Select[Prime[Range[200]], Divisible[14^(# - 1) - 1, #^2] &] (* _Alonso del Arte_, Apr 20 2014 *)
%t Select[Prime[Range[200]],PowerMod[14,#-1,#^2]==1&] (* The program generates the first two terms of the sequence. To generate the third term, increase the Range constant to 351*10^5, but the program will take a long time to run. *) (* _Harvey P. Dale_, Jun 19 2021 *)
%o (PARI)
%o N=10^9; default(primelimit, N);
%o forprime(n=2, N, if(Mod(14, n^2)^(n-1)==1, print1(n, ", ")));
%Y Cf. A001220.
%K nonn,hard,bref,more
%O 1,1
%A _Felix Fröhlich_, Apr 19 2014
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