费马测试（Fermat test）
Some of the cryptographic algorithms make use of big prime numbers. However, checking if a big number is prime is not so easy. However, some probabilistic tests exist that offer high confidence at low cost. One of them is the Fermat test.
Let $a$ be a random number between $2$ and $n-1$ (being $n$ the number whose primality we are testing). Then, $n$ is probably prime if the following equation holds:
$$a^n \bmod n = a$$
If a number passes the Fermat test several times then it is prime with a high probability.
费马小定理
若 $p$ 是素数，则对任意正整数 $x$ 都有
$$x^p \equiv x \pmod{p}$$