Prime Number Theorem

The Prime Number Theorem describes the average rate at which prime numbers thin out. In a common form, $\pi(x)\sim x/\log x$ as $x$ grows.

It captures the broad trend in the distribution of primes, but not every fluctuation. The Riemann Hypothesis would give much sharper control over the error around that average behaviour.

See also: prime-counting function, distribution of primes, Riemann Hypothesis, asymptotic..