Definition:Prime Number/Definition 4

Definition
A prime number $p$ is an integer greater than $1$ that has no positive integer divisors other than $1$ and $p$.

That is:


 * $\Bbb P = \set {p \in \N: \forall x \in \N, x \ne 1, x \ne p: x \nmid p}$

Also see

 * Equivalence of Definitions of Prime Number