Wilson's theorem

Wilson's theorem is a theorem of number theory. Let n be any natural number. Wilson's theorem says that n is a prime number if and only if:

${\displaystyle (n-1)!\ \equiv \ -1{\pmod {n}}}$

This means that if n is a prime number, the equation is correct. Also, if the equation is correct, then n is a prime number. The equation says that the factorial of (n - 1) is one less than a multiple of n.