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Prime number

Number theory

A positive integer greater than 1 whose only positive divisors are 1 and itself, equivalently an integer with exactly two distinct positive divisors.

What is usually left out

The exclusion of 1 is a convention with a reason: it makes factorisation into primes unique. If 1 counted, every number would have infinitely many factorisations. Note also that "divisible only by 1 and itself" is false read over all integers, since every prime p is also divisible by −1 and −p.

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