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.

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