Noun
Wall-Sun-Sun prime (plural Wall-Sun-Sun primes)
(number theory) A (hypothetical) prime number
p
{\displaystyle p}
such that
p
2
{\displaystyle p^{2}}
divides
F
π
(
p
)
{\displaystyle F_{\pi (p)}}
, where
F
n
{\displaystyle F_{n}}
is the Fibonacci sequence and
π
(
p
)
{\displaystyle \pi (p)}
is the
p
{\displaystyle p}
th Pisano period (the period length of the Fibonacci sequence reduced modulo
p
{\displaystyle p}
).
Wall-Sun-Sun primes are conjectured to exist, but no example has yet been found.
Synonym: Fibonacci-Wieferich prime