#11475: improve prime_pi (speedup + small fixes)
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Reporter: rohana | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: number theory | Keywords: primes, prime counting, prime_pi
Work_issues: | Upstream: N/A
Reviewer: | Author: R. Andrew Ohana
Merged: | Dependencies:
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Comment(by rohana):
Replying to [comment:8 leif]:
> Andrew, do you have some examples of wrong prime counts (beyond 2^49^),
and if so, on what kind of systems does one experience them?
{{{
sage: time prime_pi(9.75*10**15)
272450165623660
Time: CPU 25614.37 s, Wall: 25614.47 s
}}}
The correct value is `272450167482953`
(http://www.ieeta.pt/~tos/primes.html). I also computed `prime_pi(10**16)`
but in a moment of confusion, I killed the process before I grabbed the
value. If you want it I can start running it again with my current version
of the code (~3-5% faster than the latest patch).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:16>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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