Prime number theorem

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The prime number theorem is the name given to several theorems that provide estimates of the number of primes less than or equal to any given number:

Let π(n) be the prime counting function providing the number of primes less than or equal to n, for any positive number n. The simplest form of the prime number theorem states that

$\pi (n)\sim {\frac {n}{\ln n}}$.

That is, as n tends to infinity, the relative error between π(n) and n/(ln n) tends to zero. This can be expressed using limit notation as

$\lim _{n\to \infty }{\frac {\pi (n)}{n/\ln(n)}}=1$