Finite prime field

Definition

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

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

For any prime number $p$, there is a unique finite prime field of size $p$, and this is denoted $\mathbb {F} _{p}$ or $GF(p)$. This is the prime subfield (i.e., the unique smallest subfield) in any field of characteristic $p$.