Prime number theorem

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 a 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

<math>\pi(n)\sim\frac{n}{\ln n}</math>.

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

<math>\lim_{n\to\infty}\frac{\pi(n)}{n/\ln(n)}=1,</math>