π§ͺ Wall-Sun-Sun Prime (Fibonacci-Wieferich Prime) Tester
Enter a positive integer n (best for primes 7β100,000; none known to exist):
Definition: A prime p > 5 is WallβSunβSun (Fibonacci-Wieferich) if pΒ² divides Fp β Ξ΅ where Ξ΅ = (5/p) Legendre symbol.
β’ Ξ΅ = +1 if p β‘ Β±1 (mod 5) β check Fpβ1 β‘ 0 mod pΒ²
β’ Ξ΅ = β1 if p β‘ Β±2 (mod 5) β check Fp+1 β‘ 0 mod pΒ² No such primes are known (searched far beyond 10ΒΉβ΄); expect βNOβ every time.
Auto-Test checks these small/interesting primes: small ones, Fibonacci primes, and known Wieferich primes (1093, 3511).