20080908, 22:56  #1 
Jul 2008
San Francisco, CA
3·67 Posts 
GIMPS emotions and random observations
Last night at 2 am my computer finished its (my) first two LL tests ever. I told myself I wouldn’t get up in the middle of the night to check it, but like clockwork I woke up at 1:50. The past month has been something of a roller coaster, from the new learning curve, to the worry over meltdown on really hot days, to the panic of two weatherrelated power outages, to the impending discovery of M45 and 46. I never imagined I would get so caught up in it. I’m disappointed my numbers weren’t prime, but I knew the odds weren’t good going in. So, presumably, like many of you, I think my new interest will be moving myself up the producers list (woo hoo). The cost of electricity is also starting to consume more of my thoughts, and I’m seeing the value of pulling the plug on two older systems and maybe replacing them with a nehalem system in the fall. I presume everyone goes through these phases....when does it end?
As for observations, I’m surprised the calculation doesn’t use much ram. At first I read a lot of comments like “feed it as much ram as you can,” so I built a 2Gb system. Short of the one stage where it will use a lot, it doesn’t ever use much over 50 Mb (and that’s for 2 instances). Then I read the readme file by George where it says all this and felt stupid :) Will the code stop if a factor is found? I suspect the algorithm does not work this way, because both my calculations made it to 100% before declaring my numbers weren’t prime. I guess I don’t understand this part. 
20080908, 23:25  #2  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4267_{10} Posts 
Quote:
See http://www.mersenne.org/math.htm under "LucasLehmer testing" (the rest of that page is interesting reading for info on the rest of the tests GIMPS runs, but the LL test is the part that takes the longest that proves primality) and http://en.wikipedia.org/wiki/Lucas%E...rsenne_numbers for more info. 

20080909, 06:04  #3  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
Death cures addictions, if nothing else does beforehand. Quote:
There are four different types of testing in GIMPS software (Prime95/mprime): trial factoring, P1 factoring, ECM factoring and the LucasLehmer test. (However, your two assignments included only the LL type.) The answer to your question for each of those types is, respectively, TF: yes, and could be at any stage (1% to 99 %). P1 & ECM (these are the only types that use lots and lots of RAM): yes, but it can find a factor only after 100% of a computation is completed. LL: it never actually finds a factor, but after 100% of a long computation is completed it can tell you definitely whether or not some factor exists. For a GIMPS novice that may be confusing, because your assignments so far apparently included only the fourth type, LL testing. That's the most timeconsuming type, and we need the most help with it, so most active GIMPS assignments at any given time are of that type. OTOH, LL testing is the only type that can open the door to eternal mathematical fame, and a bit of mortal fortune, because it's the only type that can find a Mersenne prime! Last fiddled with by cheesehead on 20080909 at 06:07 

20080909, 13:28  #4 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10AB_{16} Posts 
Unless you consider the possibility of trial factoring every possible factor, but that would take an EXTREMELY long amount of time (much, much longer than an LL test, but it can stop at any time if it finds a factor), as each higher bit level doubles the time spent on that level, and must go to about half the exponent (normally at GIMPS's current level it goes to about 68, to prove primality by TFing along would require about 21952114) to be completely proven.

20080910, 04:28  #5  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Quote:
It isn't, for any Mersenne that is currently unfactored (say, 2^{1061}1). 2^{32582657}1 (the 44th Mersenne prime) is, by most standards of everyday life, an "EXTREMELY large" number. But the time its LL test took (6 days for the verification run) is nothing compared to the time needed to TF mere 2^{1061}1 all the way to its square root. Quote:
By letting the novice imagine that you may mean only, say, a million times as long as an LL test, you fail to convey the limitations of the trial factoring method. Here's a posting in which I presented the numerical impossibility of TFing a small Mersenne number all the way to its square root: http://mersenneforum.org/showpost.ph...10&postcount=9 Quote:
Quote:
TF to 99 bits would take about 2^{31} times as long as TF to 68 bits. Suppose TFing 2^{1061}1 to 68 bits took only, say, one hour (faster than current GIMPS computers can manage). Then TF to 99 bits would take 2^{31} hours. That's over 240,000 years. But if this were being done on 2^{1061}1, TF to 99 bits would take us less than one 2^{430}th of the way to the square root of 2^{1061}1. What's 2^{430} * 240,000 years? Over 2^{410} times the estimated age (13 billion years) of the known universe! Now, how much longer than that would it take to do that TFingtothesquareroot on a Mersenne with an exponent in the fortymillions than for one with an exponent of just 1061? Last fiddled with by cheesehead on 20080910 at 04:51 

20080910, 04:48  #6  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}·5·307 Posts 
Quote:
But what if we consider Moores law? Assume the most optimistic prediction of computer transistors (and thus core count) doubling each 18 months. Take the figure of factoring up to 2^{68} in 1 hour. My quick back of envelope calculation gives ~673 years to reach 2^{530.5}. Not so long really, and the level of patience is much less than we first assumed. Last fiddled with by retina on 20080910 at 05:35 

20080910, 05:01  #7 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
What if we consider the limits of Moore's law (which isn't a law like the laws of physics, anyway)? The doubling can't go on for more than another few tens of times, certainly not more than the maximum lifetime of any current GIMPS participant.
(Considering quantum mechanics, the Planck time and so forth, see http://mersennewiki.org/index.php/Lu...le_Explanation for some related numbers.) Last fiddled with by cheesehead on 20080910 at 05:07 
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