The prime_pi function is currently a symbolic function that can hold its argument as in

sage: n = SR.var('n')
sage: prime_pi(n)
prime_pi(n)

that also contains the Cython code for evaluating it

sage: prime_pi(13543)
1603

Unfortunately, it is buggy, see #24960 (fixed in #32894, using this ticket). We will promote the spkg primecount to standard and use it instead. This ticket does this part, and reverts deprecations from #32412. It also removes obsolete deprecation warning, and the corresponding no longer available parameter.

Upstream patch: kimwalisch/primesieve#107 (rejected)

Below is the original part, no longer too relevant.

We move the evaluation part as a standalone function in arith/ and provide alternative implementations

• using PARI/GP (only efficient in the range of tabulated primes)
• using the different algorithms in the library primecount that is packaged in package primecount 4.3 #24966

Upstream: Fixed upstream, but not in a stable release.

CC: @mkoeppe @miguelmarco @isuruf

Component: basic arithmetic

Author: Dima Pasechnik

Branch/Commit: b9b4eaf

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/25009