Definition:Wilson Prime

A Wilson prime is a prime number $$p$$ such that:
 * $$p^2 \backslash \left({p-1}\right)! + 1$$

where $$\backslash$$ signifies "divides" and $$!$$ is the factorial operator.

The only Wilson primes known to exist are:

$$ $$ $$

If there are any more, they must be greater than $$5 \times 10^8$$.

Also see
Wilson's Theorem states that every prime number $$p$$ satisfies:
 * $$p \backslash \left({p-1}\right)! + 1$$

However, the condition that its square also divides that same number is satisfied much more rarely.