Modular prime-counting function

Definition

Suppose $\text{[math]}$ is a positive real number, $\text{[math]}$ is a natural number, and $\text{[math]}$ is an integer. The modular prime-counting function for modulus $\text{[math]}$ and congruence class $\text{[math]}$ , denoted $\text{[math]}$ , is defined as the number of prime numbers less than or equal to $\text{[math]}$ , that are congruent to $\text{[math]}$ modulo $\text{[math]}$ .

This is an analogue of the prime-counting function.

Modular prime-counting function

Definition

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