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The following proposition provides also a very inefficient method of prooving if an integer is a prime number.

## Proposition: Wilson's Condition for an Integer to be Prime

An integer $n > 1$ is a prime number if and only if the following congruence holds:

$$(n-1)!\equiv -1\mod n.$$

### Notes

• In this equation, $(n-1)!$ denotes the factorial of $(n-1).$
• This proposition is also known as Wilson’s theorem, called after its discoverer John Wilson (1741 – 1793).

| | | | | created: 2019-05-11 19:54:19 | modified: 2019-06-22 08:49:15 | by: bookofproofs | references: [1272]

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