# 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