Wilson's theorem

Theorem on prime numbers

In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n. That is (using the notations of modular arithmetic), the factorial ( n − 1) ! = 1 × 2 × 3 × ⋯ × ( n − 1) {\displaystyle (n-1)!=1\times 2\times 3\times \cdots \times (n-1)} satisfies ( n − 1) !

From Wikipedia, under CC BY-SA. More on occurri.