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. .
See also
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
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