Definition:Prime Number/Definition 6

Definition
Let $p \in \N$ be an integer such that $p \ne 0$ and $p \ne \pm 1$.

Then $p$ is a prime number
 * $\forall a, b \in \Z: p \mathrel \backslash a b \implies p \mathrel \backslash a$ or $p \mathrel \backslash b$

where $\backslash$ means is a divisor of.

Also see

 * Equivalence of Definitions of Prime Number