\begin{definition}[Definition:Prime Number/Definition 4]
A '''prime number''' $p$ is an integer greater than $1$ that has no positive integer divisors other than $1$ and $p$.
That is:
:$\Bbb P = \set {p \in \N: \forall x \in \N, x \ne 1, x \ne p: x \nmid p}$
\end{definition}