Prime counting
= Prime counting
{title2=$\pi(x)$}
Prime counting evaluates the <prime-counting function>: it determines how many <prime numbers> do not exceed a given bound. A <number-theoretic sieve> can construct the whole table up to a moderate bound, while methods such as the <Lehmer prime-counting algorithm> group whole classes of <integers> to evaluate much larger arguments without listing every <prime number>.