Characteristic of Galois Field is Prime

Theorem

Let $\GF$ be a Galois field.

Then the characteristic of $\GF$ is a prime number.

Proof

By Characteristic of Field is Zero or Prime, it follows that $\Char \GF$ is $0$ or a prime number.

By Finite Field has Non-Zero Characteristic:

$\Char \GF \ne 0$

Thus $\Char \GF$ is a prime number.

$\blacksquare$