Definition:Prime-Counting Function

Definition
The prime-counting function is the function $\pi: \R \to \Z$ which counts the number of primes less than or equal to some real number.

That is:
 * $\displaystyle \forall x \in \R: \pi \left({x}\right) = \sum_{\substack {p \mathop \in \mathbb P \\ p \mathop \le x} } 1$

Also see

 * Prime Number Theorem