The **Prime Number Theorem** (or the PNT) is a theorem that concerns the distribution of primes and, subsequently, the gaps between primes. Its first proof date is not known.

## Statement of TheoremEdit

The theorem, formally stated, says that:

where is the number of primes up to and including . This means that for a number , the number of primes up to and including approaches divided by the the log to base e (or the natural log) of and becomes a better approximation of as grows larger. This also means that:

, where is the th prime number.