This is a paragraph in David M. Burton, "elementary number theory, seventh edition:
But I do not understand:
1- How Wilson's theorem implies the existence of an infinitude of composite numbers of the form $n! + 1$?
This is the statement of Wilson's theorem that I know:
$P$ is a prime iff $(p-1)! \equiv -1 (mod p)$
Could anyone explain this for me please?
2- I do not understand the second statement in the paragraph, especially in comparison to the first statement, does they mean that the form $n! +1$ can give us prime and composite numbers ?