Definition:Prime Number/Definition 2

Definition

Let $p$ be a positive integer.

Then $p$ is a prime number if and only if $p$ has exactly four integral divisors: $\pm 1$ and $\pm p$.

Also see

• Equivalence of Definitions of Prime Number

• Prime Number has 4 Integral Divisors

Sources

• 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Introduction $\S 6$: The division process in $I$
• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $3$: The Integers: $\S 12$. Primes