#7539: primes.p0.spkg with "prime_sieve.c" functionality
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Reporter: GeorgSWeber | Owner: rohana
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.3
Component: number theory | Keywords:
Work_issues: | Author: rohana, GeorgSWeber
Upstream: N/A | Reviewer:
Merged: |
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Comment(by kevin.stueve):
It is appropriate to give credit to the sources I used in making the
tables of offsets between prime_pi and a logarithmic integral
approximation. I used an asymptotic approximation to the logarithmic
integral provided by Fredrik Johansson and the tables of prime_pi from
http://www.primefan.ru/stuff/primes/table.html. And the idea of combining
a table of values of prime_pi and sieving for fast computation of the
prime_pi was provided by the nth prime page at
http://primes.utm.edu/nthprime/
The primefan tables are extensive, and are from a combined effort of
several individuals, including Andrey V. Kulsha, Anatoly F. Selevich, and
Tomás Oliveira e Silva. It is likely that the total computation time
required to generate these tables was many processor years.
As processor time (for the developer), hard-drive storage (for the
client), and Internet bandwidth (for the client) become cheaper and more
available, I would like to see published tables of prime_pi to expand (and
to see resources put toward such computation). It would be nice for the
number of values in the prime_pi tables in Sage to increase every few
years as the computation of the tables becomes easier for the developer
and the download and storage of the tables becomes easier for the client.
Maybe several table sizes could be offered. A standard table could be the
default for most users, but for those who are studying the distribution of
prime numbers and desire speed over extra storage space on their hard-
drive (and for bragging rights for Sage), larger tables could be offered.
A web-service could even be offered to query a very large table of values
of the prime counting function (the additional sieving could be done
either on the server or client). Of course, it would be very important to
have redundancy in such large calculations (the generation of the prime_pi
tables), as there have been incorrect values of the prime counting
function published several times in the past.
Kevin Stueve
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7539#comment:1>
Sage <http://www.sagemath.org>
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