A PARI bug results in an unreliable prime_pi

[sagetrac-fwclarke]

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| SAGE Version 3.0.5, Release Date: 2008-07-11                       |
| Type notebook() for the GUI, and license() for information.        |
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sage: [prime_pi(n) for n in [500508..500510]]
[41580, 45056, 41581]
sage: [prime_pi(n) for n in [500508..500510]]
[41580, 41581, 41581]

The problem lies with pari/gp:

sage: %gp

  --> Switching to GP/PARI interpreter <-- 

''
gp: for(n=500508, 500510, print(primepi(n)))

41580
45056
  *** primepi: not enough precomputed primes, need primelimit ~ 500510.

Component: number theory

Issue created by migration from https://trac.sagemath.org/ticket/3658

[craigcitro]

comment:1

The attached patch fixes the issue. This was a strange case -- in some cases, Pari is more than happy to return an (incorrect!) answer when you call primepi with a number larger than the prime limit. This patch fixes this in a uniform way.

[boothby]

comment:3

works for me

[sagetrac-mabshoff]

comment:4

On sage.math: oops:

sage -t -long "devel/sage/sage/libs/pari/gen.pyx"           
**********************************************************************
File "/scratch/mabshoff/sage-3.3.alpha2/devel/sage/sage/libs/pari/gen.pyx", line 7400:
    sage: pari._primelimit()
Expected:
    500000
Got:
    500519
**********************************************************************

Cheers,

Michael

[craigcitro]

Attachment: trac-3658.patch.gz

[boothby]

comment:6

+1

[sagetrac-mabshoff]

comment:7

Merged in Sage 3.3.alpha2.

Cheers,

Michael