prime number

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.

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).

see at *Riemann hypothesis*

see at *prime number theorem*

- Fermat prime
- Mersenne prime?
- twin prime?

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