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%I #7 Jun 19 2014 05:04:36
%S 3511,1006003,20771,491531
%N 2nd Wieferich prime base prime(n).
%C 2nd prime p such that p^2 divides prime(n)^(p-1) - 1.
%C 2nd prime p such that p divides the Fermat quotient q_p(p_n) = ((p_n)^(p-1) - 1)/p, where p_n = prime(n).
%C a(5) is unknown: 71 is the only known prime p that divides q_p(11).
%C If a(5) is found, the sequence continues a(6) = 863, a(7) = 3, a(8) = 7, a(9) = 2481757.
%C See additional comments, references, links, and cross-refs in A039951 and A174422.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fermat_quotient#Generalized_Wieferich_primes">Generalized Wieferich primes</a>
%e a(1) = 3511 is the 2nd Wieferich prime A001220(2).
%e a(2) = 1006003 is the 2nd Mirimanoff prime A014127(2).
%o (PARI) {default(primelimit, 10^7); for(n=1, 9, a=prime(n); c=0; forprime(p=2, 10^7, if(Mod(a, p^2)^(p-1)==1, c++; if(c==2, print1(p, ", "); next(2)))); print1(">10^7, "))} \\ _Jens Kruse Andersen_, Jun 18 2014
%Y Cf. A039951 = smallest prime p such that p^2 divides n^(p-1) - 1, A174422 = first Wieferich prime base prime(n).
%K hard,more,nonn
%O 1,1
%A _Jonathan Sondow_, Jun 20 2010, Jun 24 2010
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