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.