\begin{definition}[Definition:Prime Number/Definition 7]
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:
:$P = \set {x \in \N: \forall p, q \in \N: p, q \ne 1: x \ne p q}$
\end{definition}