If there exists a prime number p such that the following three conditions all apply:

It can test if a given number p is probably prime.

It is unknown whether there exists a prime number p such that C is also prime.

In any perfect square, the number p is always half the coefficient of x, and the constant term is equal to p.

It does this by picking a prime number p and an exponent a such that , according to a certain distribution.

For every prime number p and positive integer n, there exists a finite field with p elements.

For example, it is known that for a prime number p, the following holds:

The number p of repeated terms is called the period.

The logit of a number p between 0 and 1 is given by the formula:

This reduces the evaluation of Kloosterman sums to the case where for a prime number p and an integer .