Definition:Prime Number/Definition 7

Definition
A prime number $p$ is an integer greater than $1$ which cannot be written in the form:
 * $p = a b$

where $a$ and $b$ are both positive integers less than $p$.

That is:
 * $P = \set {x \in \N: \forall p, q \in \N: p, q \ne 1: x \ne p q}$

Also see

 * Equivalence of Definitions of Prime Number