# Contents

## Definition

A prime number is a natural number with exactly two factors: $1$ and itself.

Classically, $1$ was also counted as a prime number, but that is no longer done; it is too prime to be prime.

## Properties

### Relation to ideals

A number is prime if and only if it generates a maximal ideal in the rig $ℕ$ of natural numbers.

Prime numbers do not quite match the prime elements of $ℕ$, since $0$ generates a prime ideal but not a maximal ideal; instead they match the irreducible element?s (Wikipedia).

Revised on November 12, 2013 09:07:55 by Urs Schreiber (145.116.131.45)