Wall-Sun-Sun prime
From Wikipedia, the free encyclopedia
In number theory, a Wall-Sun-Sun prime is a certain kind of prime number which is conjectured to exist although none is known. A prime p > 5 is called a Wall-Sun-Sun prime if p² divides the Fibonacci number 
, where the Legendre symbol 
is defined as
Wall-Sun-Sun primes are named after D. D. Wall, Zhi Hong Sun and Zhi Wei Sun; Z. H. Sun and Z. W. Sun showed in 1992 that if the first case of Fermat's last theorem was false for a certain prime p, then p would have to be a Wall-Sun-Sun prime. As a result, prior to Andrew Wiles' proof of Fermat's last theorem, the search for Wall-Sun-Sun primes was also the search for a counterexample to this centuries-old conjecture.
No Wall-Sun-Sun primes are known as of 2009; if any exist, they must be > 1014. It has been conjectured that there are infinitely many Wall-Sun-Sun primes.
[edit] See also
[edit] References
- Richard E. Crandall; Carl Pomerance (2001). Prime Numbers: A Computational Perspective. Springer-Verlag. p. 29. ISBN 0-387-94777-9.
[edit] External links
- Chris Caldwell, The Prime Glossary: Wall-Sun-Sun prime at the Prime Pages.
- Weistein, Eric W., "Wall-Sun-Sun prime" from MathWorld.
- Richard McIntosh, Status of the search for Wall-Sun-Sun primes (October 2003)
