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A259909
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n-th Wieferich prime to base prime(n), i.e., primes p such that p is the n-th solution of the congruence (prime(n))^(p-1) == 1 (mod p^2).
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1
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OFFSET
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1,1
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COMMENTS
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Main diagonal of table T(b, p) of Wieferich primes p to prime bases b (that table is not yet in the OEIS as a sequence).
a(4), if it exists, corresponds to A123693(4) and is larger than 9.7*10^14 (cf. Dorais, Klyve, 2011).
a(5), if it exists, corresponds to the 5th base-11 Wieferich prime and is larger than approximately 5.9*10^13 (cf. Fischer).
a(6), if it exists, corresponds to A128667(6) and is larger than approximately 5.9*10^13 (cf. Fischer).
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REFERENCES
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W. Keller, Prime solutions p of a^p-1 = 1 (mod p2) for prime bases a, Abstracts Amer. Math. Soc., 19 (1998), 394.
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LINKS
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K. E. Kloss, Some Number-Theoretic Calculations, J. Research of the National Bureau of Standards-B. Mathematics and Mathematical Physics, Vol. 69B, No. 4 (1965), 335-336.
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EXAMPLE
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PROG
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(PARI) a(n) = my(i=0, p=2); while(i < n, if(Mod(prime(n), p^2)^(p-1)==1, i++; if(i==n, break({1}))); p=nextprime(p+1)); p
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CROSSREFS
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KEYWORD
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nonn,hard,bref,more
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AUTHOR
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STATUS
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approved
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