20081001, 23:52  #1 
Jul 2008
San Francisco, CA
3×67 Posts 
100M madness
Is it really all that crazy to contemplate this? I've been reading posts that say it would take too long with current technology to try for a 100M digit monster. Help me out here:
My current E8500 can LL a 12M digit number in about 28 days (actually it can do 2LL's in that time, but just consider 1 for now). If we assume the calculation is linear (is it?), then we're looking at about 233 days (~8 months) for a 100M digit number. That's a long time, but... Suppose we take things up a notch and run on a new Nehalem processor in a few months, where we're hoping to get true quad performance. One could run the 100M number on a single core, and run 3 other more reasonable LL's on the other cores, and still outperform todays best Penryn quad that people report getting about 3 coresworth of performance. Nehalem may even shorten the 8 month estimate. Some benchmarks put it at 30% better performance than Penryn, but I have no idea what we'll actually see on prime95. If the 30% performance gain applies to prime95, 8 months would shrink below 6 months and one could do 2 100M numbers in a year on a single core! All this boils down to linearity, so is it? 
20081002, 01:04  #2 
P90 years forever!
Aug 2002
Yeehaw, FL
2·41·89 Posts 

20081002, 01:33  #3 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
It's definitely much harder than linear. Assuming that iteration time is proportional to FFT length, the smallest 100M digit exponent would take over 61.6 times longer than 2^43112609  1.
Take a look at this (http://www.mersenneforum.org/showthr...ies#post141900). Also see (http://www.mersenneforum.org/showthread.php?t=10660), post #6. Last fiddled with by jinydu on 20081002 at 01:35 
20081002, 03:24  #4 
Jul 2008
San Francisco, CA
3·67 Posts 
Ok, I'm an idiot. All I had to do was use the benchmark page to estimate the time for my processor to test a 100M digit number. For my E8500, the estimate is 4 years, 150 days...a little long for my patience level and certainly not a linear extrapolation from my 12M digit numbers.
Regarding Nehalem, will the large L3 cache help offset the small L2? Presumably the Quickpath interconnect will get closer to allcore performance. I was really hoping to get one and move up the producers list and crush you guys. Don't burst my bubble! 
20081002, 03:32  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
176A_{16} Posts 

20081002, 06:27  #6 
Oct 2004
Austria
9B2_{16} Posts 

20081002, 10:37  #7  
Jan 2008
France
2·271 Posts 
Quote:
BTW that makes me wonder: are there processors that have different data prefetch instructions that target different memory hierarchy levels? 

20081002, 11:47  #8 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 

20081002, 15:21  #9 
"Phil"
Sep 2002
Tracktown, U.S.A.
2×13×43 Posts 
And since the number of iterations is equal to the exponent (minus 2), the total time to do a LucasLehmer test is approximately proportional to the square of the exponent. Double the exponent, quadruple the runtime.

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