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 $\mathbb{N}$ of natural numbers.

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

Riemann hypothesis

see at Riemann hypothesis

Asymptotic distribution

see at prime number theorem

Specific classes of prime numbers

Revised on April 14, 2015 02:08:17 by David Roberts (203.24.207.3)