A Wall-Sun-Sun prime is a prime number such that , with being the th Fibonacci number and being a Legendre symbol. The prime always divides , but no case is known for the square of a prime also dividing that.
The search for these primes started in the 1990s as Donald Dines Wall, Zhi-Hong Sun and Zhi-Wei Sun searched for counterexamples to Fermat’s last theorem. But Andrew Wiles’s proof does not rule out the existence of these primes: if Fermat’s last theorem was false and there existed a prime exponent such that , the square of such a prime would also divide , but with Fermat’s last theorem being true, the existence of a Wall-Sun-Sun prime would not present a contradiction.
As of 2005, the lower bound was , given by McIntosh.
- 1 Richard Crandall & Carl Pomerance, Prime Numbers: A Computational Perspective, 2nd Edition. New York: Springer (2005): 32
|Date of creation||2013-03-22 18:04:18|
|Last modified on||2013-03-22 18:04:18|
|Last modified by||PrimeFan (13766)|
|Synonym||Fibonacci Wieferich prime|