# Finite prime field

From Groupprops

(Redirected from Prime field)

## Definition

A **finite prime field** is a finite field satisfying the folloqing equivalent conditions:

- It contains no proper subfield.
- Its size is a prime number.

For any prime number , there is a unique finite prime field of size , and this is denoted or . This is the prime subfield (i.e., the unique smallest subfield) in any field of characteristic .