A "Prime Number" is a counting number that is:

Bigger than $1$
Has no positive divisors other than itself and $1$

Sometimes this is phrased as "no non-trivial divisors."

For example, every positive whole number can be expressed as the product of primes in exactly one way (up to ordering) would have to exclude 1 from being considered as a prime, otherwise it's not true, since $3=1{\times}3=1{\times}1{\times}3$.

Equivalently we can say that it is a counting number with exactly two positive divisors (specifically, itself and 1).

Historically, 1 has until fairly recently been considered to be prime, however it's now considered more convenient to exclude 1 as a prime, since it makes various statements easier.

There are still things that we don't know about prime numbers. For example, we don't know it there are infinitely many prime pairs.

See also: Composite number

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