In mathematics, a WallSunSun prime is a certain kind of prime number which is conjectured to exist although none are known. A prime p > 5 is called a WallSunSun prime if p² divides
where F(n) is the nth Fibonacci number and is the Legendre symbol of a and b. WallSunSun 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 WallSunSun prime. As a result, prior to Andrew Wiles' proof of Fermat's last theorem, the search for WallSunSun primes was also the search for a counterexample to this centuriesold conjecture. No WallSunSun primes are known as of 2008; if any exist, they must be > 1014. It has been conjectured that there are infinitely many WallSunSun primes. See also * Wieferich prime * Wilson prime * Wolstenholme prime Links * Chris Caldwell, The Prime Glossary: WallSunSun prime at the Prime Pages. * Eric W. Weisstein, WallSunSun prime at MathWorld. * Richard McIntosh, Status of the search for WallSunSun primes (October 2003) Retrieved from "http://en.wikipedia.org/"

