# nLab prime number theorem

## Idea

What is known as the prime number theorem is a description of the asymptotic distribution of prime numbers. It says that the number of primes less than a positive real number $x$ is asymptotic to $x/\log(x)$, where $\log x$ is the natural logarithm.

## Proof

See proof of the prime number theorem, which is based on a well-known account by Don Zagier (who in turn was explicating a short proof due to Donald J. Newman) – see the references there.

## References

Last revised on March 30, 2018 at 19:53:21. See the history of this page for a list of all contributions to it.