Modular prime-counting function

Definition

Suppose $x$ is a positive real number, $n$ is a natural number, and $a$ is an integer. The modular prime-counting function for modulus $n$ and congruence class $a$, denoted $\pi (x;n,a)$, is defined as the number of prime numbers less than or equal to $x$, that are congruent to $a$ modulo $n$.

This is an analogue of the prime-counting function.