Reference Database
(references for the Prime Pages)
The Prime Pages

Home
Search Site

Largest
Finding
How Many?
Mersenne

Glossary

Prime Curios!
e-mail list

FAQ
Prime Lists
Titans

Submit primes
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) 433--449.  MR 97c:11004
Abstract: An odd prime p is called a Wieferich prime if
2p-1 ≡ 1 (mod p2) ;
alternatively, a Wilson prime if
(p-1)! -1 (mod p2) .
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× 1012, and no new Wilson primes p< 5× 108. 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) .
Prime Pages' Home
Another prime page by Chris K. Caldwell