Category:Definitions/Prime-Counting Function

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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:

$\ds \forall x \in \R: \map \pi x = \sum_{\substack {p \mathop \in \mathbb P \\ p \mathop \le x} } 1$

where $\mathbb P$ denotes the set of prime numbers.