
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Fermat's "biggest", and also his "last" theorem states that x^{n} + y^{n} = z^{n} has no solutions in positive integers x, y, z with n greater than 2. This has finally been proven by Wiles in 1995. However, in the study of primes it is Fermat's little theorem that is most used: It is so easy to calculate a^{p1} that most elementary primality tests are built using a version of Fermat's Little Theorem rather than Wilson's Theorem. As usual, Fermat did not provide a proof (this time saying "I would send you the demonstration, if I did not fear its being too long" [Burton80, p79]). Euler first published a proof in 1736, but Leibniz left virtually the same proof in an unpublished manuscript from sometime before 1683.
See Also: FermatQuotient Related pages (outside of this work) Chris K. Caldwell © 19992020 (all rights reserved)
