Prime-counting function

This article is about a function defined on positive reals (and in particular, natural numbers) obtained as the summatory function of an arithmetic function, namely primality indicator function.
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Definition

Let $x$ be a positive real number. The prime-counting function $\pi (x)$ is defined as the number of prime numbers less than or equal to $x$.

Relation with other counting functions

• First Chebyshev function
• Second Chebyshev function