Prime counting

The prime counting function $\pi \colon \mathbb{R} \rightarrow \mathbb{Z}^+$ is defined by the formula $$\pi(x) = \{\mathrm{number \hspace{2pt} of \hspace{2pt} primes} \leq x \}.$$

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  Graph of $\pi(x)$.

Properties

Prime number theorem, pi and x/log(x)
Prime number theorem, logarithmic integral

References

Newman's short proof of the prime number theorem