WALL-SUN-SUN PRIME

In mathematics, a 'Wall-Sun-Sun prime' is a certain kind of prime number. A prime ''p'' > 5 is called a Wall-Sun-Sun prime if ''p''² divides
:
ight)
ight)
where ''F''(''n'') is the ''n''th Fibonacci number and
ight) is the Legendre symbol of ''a'' and ''b''.
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 2007; if any exist, they must be > 10¹⁴. It has been conjectured that there are infinitely many Wall-Sun-Sun primes.

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See also

External links

See also

★ Wieferich prime

★ Wilson prime

★ Wolstenholme prime

External links

★ The Prime Glossary: Wall-Sun-Sun prime

★ MathWorld: Wall-Sun-Sun prime

★ Status of the search for Wall-Sun-Sun primes