# Modular Arithmetic/Wilson's Theorem

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**Wilson's theorem**

A natural number is a prime number, if and only if:

Where denotes the factorial of , meaning the product of all numbers less than or equal to , for every natural number.

## Examples[edit | edit source]

5 is a prime number because,

and

which is true. 6, on the other hand, is not, as

and

which is false.