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 $$p$$.