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Re: Prime[..] slows down

• To: mathgroup at smc.vnet.net
• Subject: [mg53540] Re: [mg53524] Prime[..] slows down
• From: DrBob <drbob at bigfoot.com>
• Date: Sun, 16 Jan 2005 22:23:57 -0500 (EST)
• References: <200501160207.VAA05705@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

Timing works inside the loop just fine:

Sets = 10;
KK = 20000;
InitValue = 105000000;
Steps = 10000;
For[k = 1, k <= Sets, k++,
   Print@Timing@For[j = 1, j <= KK, j++, x = 2*Prime[InitValue + k*Steps + j]]]

{0.172 Second,Null}
{0.188 Second,Null}
{0.281 Second,Null}
{0.172 Second,Null}
{0.422 Second,Null}
{0.203 Second,Null}
{0.172 Second,Null}
{0.906 Second,Null}
{2.641 Second,Null}
{4.187 Second,Null}

or

Sets=10;
KK=20000;
start=105000000;
Steps=10000;
limits={First@#,Last@#}&;
Do[start+=Steps;
   Print@{start+1,start+KK,First@Timing@
         Do[2*Prime@i,{i,start+1,start+KK}]},{Sets}]

{105010001,105030000,0.11 Second}
{105020001,105040000,0.093 Second}
{105030001,105050000,0.219 Second}
{105040001,105060000,0.094 Second}
{105050001,105070000,0.344 Second}
{105060001,105080000,0.14 Second}
{105070001,105090000,0.094 Second}
{105080001,105100000,0.813 Second}
{105090001,105110000,2.562 Second}
{105100001,105120000,4.047 Second}

As for why Prime slows down... it clearly HAS to slow down as the argument gets larger; precisely when and how much can depend on all sorts of implementation details we're not privy to.

Bobby

On Sat, 15 Jan 2005 21:07:53 -0500 (EST), George Szpiro <george at netvision.net.il> wrote:

>
> My last posting did not have the program listing:
>
>
> can somebody explain why Prime[...] slows down so drastically and so
> abruptly at about 105
> million (see below)?
>
> also: how can I get elapsed time in fractions of seconds? (Timing[...] did
> not work inside the loop for some reason.)AboluteTime to give
>
> Thanks,
>
> George
> george at netvision.net.il
>
>
>
>
> Sets=100;
>
> KK=20000;
>
> InitValue=105000000;
>
> Steps=10000;
>
> For[k=1,k<=Sets,k++,
>
>   TT=AbsoluteTime[];
>
>   For[j=1,j<=KK,j++, x=2*Prime[InitValue+k*Steps+j];]
>
>
>
>     Print["Prime[",InitValue+k*Steps+j-1,"]=",Prime[InitValue+k*Steps+j-1],"
> Time ",AbsoluteTime[]-TT];
>
>   TT=AbsoluteTime[];]
>
>
>
>
>
>
> Prime[105010000]=2145604099 Time 1.00000
>
> Prime[105030000]=2146031753 Time 2.00000
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net

• References:
  • Prime[..] slows down
    • From: George Szpiro <george@netvision.net.il>