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# Wall-Sun-Sun Prime

Let be the th Fibonacci number, and let be a Legendre symbol so that

 (1)

A prime is called a Wall-Sun-Sun prime if

 (2)

The first few values of are 2, 3, 5, 21, 55, 39, 272, 57, ... (OEIS A113650).

There are no Wall-Sun-Sun primes up to a limit of (McIntosh 2004), subsequently extended to by PrimeGrid as of November 2015.

Let be the th Lucas number. Then

 (3)

for all primes . The first few values of are 2, 7, 0, 47, 2, 167, 287, ... (OEIS A113651).

Let be prime. Then the following are equivalent:

1. ,

2. ,

3. .

Fibonacci Number, Integer Sequence Primes, Lucas Number

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## References

McIntosh, R. email to Paul Zimmermann. 9 Mar 2004. http://www.loria.fr/~zimmerma/records/Wieferich.status.PrimeGrid PRPNet. "Wall-Sun-Sun Prime Search." http://prpnet.primegrid.com:13001.Sloane, N. J. A. Sequences A113650 and A113651 in "The On-Line Encyclopedia of Integer Sequences."

## Referenced on Wolfram|Alpha

Wall-Sun-Sun Prime

## Cite this as:

Weisstein, Eric W. "Wall-Sun-Sun Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Wall-Sun-SunPrime.html