#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
Component: number theory | Keywords: primes, sieve, table,LMO
Work_issues: | Author: Kevin Stueve
Upstream: N/A | Reviewer: was,robertwb,GeorgSWeber
Merged: |
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Comment(by kevin.stueve):
I noticed on line 506 of "sage/functions/prime_pi.pyx" in the patch that
prime_pi(x) is capped at x=2**61 (2.30584301 × 10**18). This is okay if
the LMO code is used for the largest values of x. However, without the
LMO code being called in such cases, the table/sieving prime_pi will start
to return incorrect values as soon as the li(x)-pi(x) values don't fit
within three bytes (somewhere between 10**17 and 10**18, see my above post
on this issue I made two months ago).
The options are:[[BR]]-cap the allowed values of x so that li(x)-pi(x)
will never exceed three bytes of space[[BR]] -modify the table to allow
more than three bytes of storage when necessary[[BR]] -incorporate the LMO
code for large values of x
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7013#comment:18>
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