#11475: improve prime_pi (speedup + small fixes)
-----------------------------+----------------------------------------------
   Reporter:  rohana         |          Owner:  was                             
       Type:  enhancement    |         Status:  needs_review                    
   Priority:  major          |      Milestone:  sage-4.7.1                      
  Component:  number theory  |       Keywords:  primes, prime counting, prime_pi
Work_issues:                 |       Upstream:  N/A                             
   Reviewer:                 |         Author:  R. Andrew Ohana                 
     Merged:                 |   Dependencies:                                  
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Comment(by leif):

 I've so far only tested a little (on 64-bit Linux; dead old 32-bit box
 still building Sage), but already found one wrong result '''with patch
 v3''':

 {{{
   502000000000000  15296923904889   # 11475v3
   502000000000000  15296922045596   # correct result, (at least) double-
 checked
 }}}

 Note that 502*10^12^ is ''below'' 2^49^ (562.949.953.421.312).

 As my machines are still busy, you could perhaps check if the newer
 version(s) give the correct result.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11475#comment:21>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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