Ok, I would suggest we do the following:
* In 3.4.2 cap prime_pi at 2^40 since that is what Andrew suggests as correct range for his algorithm * add the following #long doctest (it takes about 25 seconds total in sage.math): sage: for n in (30..40): ....: time prime_pi(2^n) <SNIP results> * For the range of 2^40+1 to 2^46 I am uncomfortable to have it available per default, especially if we don't at least spot check the values via doctesting and it would be getting slow to do so - even for #long. But we could add some keyword to force the upper limit up to a 2^46 - the issue should be revisited post 3.4.2 - maybe even implementing a better algorithm? * In 3.4.1 prime_pi() was completely broken for even 2^35 because len (prime_range(2^35)) aborts on sage.math since pari fails to allocate 124 *GB* of memory. That implementation is actually about 2000 times slower than what Andrew wrote. I have no idea why pari's primes_up_to_n or whatever it is called internally is so extremely inefficient. Maybe somebody out to check pari-svn and complain? As mentioned on the other ticket (#5943) the prime_range(2^50) outright segfaults even in 3.4.2.final. Thoughts? Cheers, Michael --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
