Wall-Sun-Sun prime

plural Wall-Sun-Sun primes · alternative Wall-Sun-Sun prime number

1. mathematicsA (hypothetical) prime number p such that p² divides F_π(p), where F_n is the Fibonacci sequence and π(p) is the pth Pisano period (the period length of the Fibonacci sequence reduced modulo p).

   Wall-Sun-Sun primes are conjectured to exist, but no example has yet been found.

   2 more examples

   Not a single Wall-Sun-Sun prime 5lt;plt;1.6#92;times 10#123;12#125; exists [McIntosh 1995]. Carry out a search for Wall-Sun-Sun primes somewhere above this limit.

   1996, Richard E. Crandall, Topics in Advanced Scientific Computation, Springer, page 113

   Crandall et al. called in [56] such a prime number p satisfying p²#92;vertF#95;#123;p-(#92;fracp 5)#125; a Wall–Sun–Sun prime. There is no known example of a Wall–Sun–Sun prime and the congruence F#95;#123;p-(#92;fracp 5)#125;#92;equiv 0#92;pmod#123;p²#125;, can only be checked through explicit powering computations.

   2020, Dorin Andrica, Ovidiu Bagdasar, Recurrent Sequences, Springer, page 88

   Synonyms: Fibonacci-Wieferich prime