Prime Factorial

While doing some random computing I accidently found out something.

(2!+1)/3=1
(3!+1)/4=Fraction
(4!+1)/5=5
(5!+1)/6=Fraction
(6!+1)/7=103

Only when the denominator is a prime the quotient will be an integer.

Let n be prime
Then ((n-1)!+1)/n will be an integer.

I computed it to really large numbers and seemed to hold.

Don't yet know if its generally true.

Update: This theorem is called Wilson's Thoerem.