On Sun, May 3, 2009 at 9:23 AM, Dr. David Kirkby
<david.kir...@onetel.net> wrote:
>
> Here's a table of PrimePi[2^n], with n ranging from 0 to 47. It took
> roughly 20 minutes or so to compute the table.
>
> In[19]:= Table[{n,PrimePi[2^n]},{n,0,47}]
>
> Out[19]= {{0, 0}, {1, 1}, {2, 2}, {3, 4}, {4, 6}, {5, 11}, {6, 18}, {7, 31},
>
> > {8, 54}, {9, 97}, {10, 172}, {11, 309}, {12, 564}, {13, 1028},
>
> > {14, 1900}, {15, 3512}, {16, 6542}, {17, 12251}, {18, 23000},
>
> > {19, 43390}, {20, 82025}, {21, 155611}, {22, 295947}, {23, 564163},
>
> > {24, 1077871}, {25, 2063689}, {26, 3957809}, {27, 7603553},
>
> > {28, 14630843}, {29, 28192750}, {30, 54400028}, {31, 105097565},
>
> > {32, 203280221}, {33, 393615806}, {34, 762939111}, {35, 1480206279},
>
> > {36, 2874398515}, {37, 5586502348}, {38, 10866266172},
>
> > {39, 21151907950}, {40, 41203088796}, {41, 80316571436},
>
> > {42, 156661034233}, {43, 305761713237}, {44, 597116381732},
>
> > {45, 1166746786182}, {46, 2280998753949}, {47, 4461632979717}}
>
For the record, here's the same thing in Sage. As you can see, it
took slightly less than 30 minutes on a macbook.
sage: time [[n, prime_pi(2^n)] for n in range(48)]
CPU times: user 1727.90 s, sys: 0.78 s, total: 1728.69 s
Wall time: 1737.05 s
[[0, 0],
[1, 1],
[2, 2],
[3, 4],
[4, 6],
[5, 11],
[6, 18],
[7, 31],
[8, 54],
[9, 97],
[10, 172],
[11, 309],
[12, 564],
[13, 1028],
[14, 1900],
[15, 3512],
[16, 6542],
[17, 12251],
[18, 23000],
[19, 43390],
[20, 82025],
[21, 155611],
[22, 295947],
[23, 564163],
[24, 1077871],
[25, 2063689],
[26, 3957809],
[27, 7603553],
[28, 14630843],
[29, 28192750],
[30, 54400028],
[31, 105097565],
[32, 203280221],
[33, 393615806],
[34, 762939111],
[35, 1480206279],
[36, 2874398515],
[37, 5586502348],
[38, 10866266172],
[39, 21151907950],
[40, 41203088796],
[41, 80316571436],
[42, 156661034233],
[43, 305761713237],
[44, 597116381732],
[45, 1166746786182],
[46, 2280998753949],
[47, 4454203917918]]
And as mentioned before, the values up to 46 are correct, and the
value at 47 is wrong.
> PS, Mathematica computes PrimePi[some_negative_number] as 0. Does Sage
> handle that case ok?
>
sage: prime_pi(-20)
0
--
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
-- Australia -- http://www.ms.unimelb.edu.au/~aghitza/
--~--~---------~--~----~------------~-------~--~----~
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
-~----------~----~----~----~------~----~------~--~---
