#7013: [with patch, needs work] prime_pi and nth_prime
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Reporter: kevin.stueve | Owner: kevin.stueve
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: number theory | Keywords: primes, sieve, table,LMO
Author: Kevin Stueve | Upstream: N/A
Reviewer: was,robertwb,GeorgSWeber | Merged:
Work_issues: |
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Old description:
> Computes the prime counting and nth prime function. This is my first
> Sage contribution.
>
> http://sage.math.washington.edu/home/robertwb/tmp/KevinStueve.tar.lzma
> http://sage.math.washington.edu/home/kstueve/KevinStueve.zip
> http://docs.google.com/View?id=df9q29vh_42dwz388hp
New description:
Computes the prime counting and nth prime function. This is my first Sage
contribution.
http://sage.math.washington.edu/home/robertwb/tmp/KevinStueve.tar.lzma
http://sage.math.washington.edu/home/kstueve/KevinStueve.zip
http://docs.google.com/View?id=df9q29vh_42dwz388hp
''''''
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Comment(by leif):
Replying to [comment:47 kevin.stueve]:
> I updated our prime counting code to use denser tables from TOS, TRN,
and Kulsha, and an updated version of TOS's prime_sieve.c from Leif.
Note that this version of {{{prime_sieve.c}}} is outdated (and btw, it
should be called {{{prime_pi_sieve_tos.c}}}).
I hope I can provide a slightly polished version of the latest (Jan 2010,
with optimizations, all overflow conditions I'm aware of - see #7539 -
fixed) within this week.
> Right now the interval [1e14,1e15] has spacing 1e10. It would be nice,
and not too difficult to sieve this interval with prime_sieve.c on
Sagemath with spacing 1e9. This would be good to compare against Andrew
Booker's new data he is going to calculate.
Regarding the current density in other ranges, I'd consider this rather a
waste of time and space; even with - nowadays suboptimal - LMO, it takes
only a few seconds to compute pi(x) in that range.
Above 10^19^ we have a spacing of 10^16^, which is far too sparse; I'm
currently computing pi(N*10^15^) for N>10000 (hopefully up to N=18446,
i.e. 2^64^, but this will take months...).
>
http://sage.math.washington.edu/home/kstueve/uploads/March21_2010/TableBasedPrimePi.zip
'''Please''' separate the data from the code... ;-)
-Leif
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7013#comment:48>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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