Wilson prime

A Wilson prime is a special kind of prime number. A prime number "p" is a Wilson prime if (and only if [ iff ])
formula_1
where "n" is a positive integer (sometimes called natural number). Wilson primes were first described by Emma Lehmer.
The only known Wilson primes are 5, 13, and 563 ; if any others exist, they must be greater than 5. It has been conjectured that there are an infinite number of Wilson primes, and that the number of Wilson primes in an interval is about
formula_2.
Compare this with Wilson's theorem, which states that every prime "p" divides ("p" − 1)! + 1.