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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:
$$(n-1)!\equiv -1\mod n.$$
- 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).
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- Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927