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 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

.

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