Function: primepi
Section: number_theoretical
C-Name: primepi
Prototype: G
Help: primepi(x): the prime counting function pi(x) = #{p <= x, p prime}.
Description:
(gen):int primepi($1)
Doc: the prime counting function. Returns the number of
primes $p$, $p \leq x$.
\bprog
? primepi(10)
%1 = 4;
? primes(5)
%2 = [2, 3, 5, 7, 11]
? primepi(10^11)
%3 = 4118054813
@eprog\noindent Uses checkpointing and a naive $O(x)$ algorithm;
make sure to start gp with \kbd{primelimit} at least $\sqrt{x}$.