The prime counting function is a non-multiplicative function for any positive real number $x$ denoted as $\pi(x)$ and gives the number of primes not exceeding $x$ It usually takes a positive integer $n$ for an argument. The first few values of $\pi(n)$ for $n = 1, 2, 3, \ldots $ are $0, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8 \ldots $ (OEIS A000720 ).

The asymptotic behavior of $\pi(x) \sim x/\ln x$ is given by the prime number theorem. This function is closely related with Chebyshev's functions $\vartheta(x)$ and $\psi(x)$