#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-4.3.2
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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Comment(by kevin.stueve):
I have an idea to use MD5 hash to detect machine rounding differences in
the table compression, which combines several of our ideas. Store
offsets/differences/whatever (either for values, intervals, or whatever
the method is) without regard for rounding errors or storing parity bits.
But store the MD5 hash of either the entire table, or chunks of it. Do a
one time unpacking of either the entire table or chunks of it, and at this
time, compare the stored MD5 hash against the MD5 hash of the unpacked
table. It is not necessary for the hash to be cryptographically secure,
because we are only checking file integrity. If the MD5 hash values do not
match, display a fatal error message, describing that the system has
unexpected floating point properties, and that a (larger) table that does
not depend on floating point needs to be downloaded, with
instructions/link (or perhaps tries to download it automatically, with
permission to access the Internet). Even if this idea doesn't make it into
Sage's production prime_pi, it would be useful for a demo of the
compression that would result from using the Riemann correction terms (see
#8135). For an idea of the compression possible, see Patrick Demichel's
"The prime counting function and related subjects" (link at bottom of
wikipedia's Skewes' number page).
Kevin Stueve
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7013#comment:43>
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