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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 CDP97
 R. Crandall, K. Dilcher and C. Pomerance, "A search for Wieferich and Wilson primes," Math. Comp., 66:217 (1997) 433449. MR 97c:11004
Abstract:
An odd prime p is called a Wieferich prime if 2^{p1} ≡ 1 (mod p^{2}) ; alternatively, a Wilson prime if (p1)!≡ 1 (mod p^{2}) . To date the only known Wieferich primes are p=1093 and 3511, while the only known Wilson primes are p=5, 13, and 563. We report that there exist no new Wieferich primes p< 4× 10^{12}, and no new Wilson primes p< 5× 10^{8}. It is elementary that both defining congruences above hold merely (mod p) , and it is sometimes estimated on heuristic grounds that the "probability" that p is Wieferich (independently: that p is Wilson) is about 1/p. We provide some statistical data relevant to occurrences of small values of the pertinent Fermat and Wilson quotients (mod p) .
