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Wilson's theorem

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necessary and sufficient condition for a number to be prime

~11 min read

Encyclopedic overview

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 )

Excerpted from Wikipedia’s “Wilson's theorem” article, available under the CC BY-SA 4.0 licence.