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:

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

See Also

• Euler Phi Function

• Prime Number Theorem