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.