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 if and only if

$\forall a, b \in \Z: p \divides a b \implies p \divides a$ or $p \divides b$

where $\divides$ means is a divisor of.

Also see

• Equivalence of Definitions of Prime Number

Sources

• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.1$. Arithmetic: Definition