Wilson quotient

The Wilson quotient is a concept in number theory related to Wilson's theorem. Wilson's theorem states that a natural number \( p \) is a prime if and only if \[ (p-1)! \equiv -1 \, (\text{mod } p). \] The Wilson quotient is computed using the factorial of \( p-1 \) and is specifically defined for prime numbers. It can be expressed as: \[ W(p) = \frac{(p-1)!