20110403, 17:06  #1 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2×283 Posts 
Trial Factoring vs. LLtesting
Here follows some statistics from my last days work.
I have been doing trial factoring ^68 > ^69 for 906 exponents in the range 53 400 000 to 55 200 000. The total factoring costs have been 979.86 GHzDays and among the 906 exponents have 12 factors been found. Doing first trial LLtest would have costed 12 * 110 GhzDays = 1320 GHzDays. And the doublecheck as much. That is a total of 2640 GHzDays. Roughly speaking, trial factoring the same number of 906 exponets ^69 > ^70 would cost more or less twice as much = 1960 GHzDays. But most probably we would find another 12 factors of these exponents, but the saving would be as large. Roughly 2650 GHzDays. So, the question is: Why don't we do it? I gather there is something I don't understand here? 
20110403, 18:15  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
11×389 Posts 
FYI for everyone: Prime95 will TF to 2^69 for exponents this size.
It's possible that the TF limits need to be adjusted, but here's something to consider: P1 is usually run before the last bit of TF. P1 can find some factors that might have otherwise been discovered via TF, so the probability of TF finding a factor after P1 has been run is lower. Let's say you're looking at a group of 1000 exponents, average p=54,300,000 that have been TF'd to 2^69 and have P1 searches whose probabilities of finding factors averaged 0.07 (7%), and you want to know if TFing to 2^70 should save time. For each TF, you can expect to find 0.0145988 factors, so for 1000 TFs, you can expect to find 14.5988. But about 7% (I doubt this is precisely accurate, probably a bit more, but it should be close enough for this estimation) of those were already found by P1, so you can expect to find 13.5767 new factors. This will take about 2.2019 GHzdays for each one, or 2201.91 GHzdays total. One LL test takes 115.09 Ghzdays, and you can expect to run a little over 2 LLs per exponent due to DCing and nonmatching residues, say 2.1. That's 241.68 GHzdays saved if you can find a factor. With the factors we expect, that's 3281.26 GHzdays. This means you can expect to save 1079.35 GHzdays by TFing. So my calculations agree with yours, assuming GHzdays are accurate whether TFing or LLing: exponents that size should be tested to 2^70. (take my calculations with a large grain of salt  assumptions, too many significant digits shown, possible mistakes, etc. mean it's anything but precise  but I think the conclusion is quite possibly valid) Keep in mind that's only 1.079 GHzdays saved per exponent. That's on the order of half a percent more efficient. A little LL efficiency improvement ups the speed of the project way more than this. Still, on the scale of GIMPS, no point having any waste. (p.s. for reference, many of the figures came from the very handy tools at http://mersennearies.sili.net/credit.php) Last fiddled with by TimSorbet on 20110403 at 18:25 
20110404, 01:47  #3 
P90 years forever!
Aug 2002
Yeehaw, FL
5·23·71 Posts 
The trial factoring vs. LL testing breakeven points were last calculated for a 2.0 GHz Pentium 4.
I'll play around using a Core 2 machine to see if the breakeven points need to change much. 
20110404, 03:04  #4 
Dec 2010
Monticello
5×359 Posts 
The problem I see with this is that we now have a sufficiently heterogeneous population (GPUs versus CPUs), and GPUs are sufficently more efficient than CPUs at TF that the *cost* of a GHzday of TF on a GPU is significantly less than on a CPU. I don't see my single CPU core catching up with a reasonable GPU, designed for parallelism, any time soon.
I even have a (cheap) GPU that doesn't have the ability to do LL! 
20110404, 03:18  #5  
P90 years forever!
Aug 2002
Yeehaw, FL
1111111100101_{2} Posts 
Quote:


20110404, 03:33  #6  
P90 years forever!
Aug 2002
Yeehaw, FL
1FE5_{16} Posts 
Quote:
New breakevens: #define FAC79 516800000L #define FAC78 408400000L #define FAC77 322100000L #define FAC76 253500000L #define FAC75 199500000L #define FAC74 153400000L #define FAC73 120000000L #define FAC72 96830000L #define FAC71 77910000L #define FAC70 60940000L #define FAC69 48800000L #define FAC68 38300000L #define FAC67 29690000L Old breakevens: //#define FAC80 516000000L //#define FAC79 420400000L //#define FAC78 337400000L //#define FAC77 264600000L //#define FAC76 227300000L //#define FAC75 186400000L //#define FAC74 147500000L //#define FAC73 115300000L //#define FAC72 96830000L //#define FAC71 75670000L //#define FAC70 58520000L //#define FAC69 47450000L //#define FAC68 37800000L //#define FAC67 29690000L I'll modify version 26.6 to reflect the new Core 2 breakeven points (which will have virtually no effect as most LL assignments have already had all necessary TF completed). For now, I'll not change the server. In fact, we have so much excess TF capacity, there has been serious thought given to having the server assign an extra bit of TF. 

20110404, 04:44  #7  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2·7·13·29 Posts 
Quote:
If you can't tell could it be an option to have another work type of TFGPU? Mind you, it would have to be on the honor system. i.e. If I ask for TFGPU and don't have a GPU or don't run it ona GPU that would be MY problem. 

20110404, 07:00  #8  
Dec 2007
Cleves, Germany
1000010010_{2} Posts 
Quote:


20110405, 01:39  #9  
Dec 2010
Monticello
3403_{8} Posts 
Quote:
That is, minimizing GHz days is a standin for the real objective (roughly, finding the most Mersenne Primes at the least cost in time and other factors, such as electrical energy) works until we have machines like the GPUs that run circles around our original CPU machines, but only for some kinds of work. I suggest that we make it easier in lots of ways to put GPUs to other kinds of useful work. This includes NFS@home, making sure normal folks can find the latest LL for CUDA, and thinking seriously (RDS: Flame off please, I am ignorant here and we might already know these aren't good ideas) about P1 and ECM on CUDA. **** If this is a bit hard to visualize, recalculate the balance of TF and LL to get the optimum cost in calendar time if your favorite highend CUDAenabled GPU is assigned both the TF and the firsttime and doublecheck LL for your favorite candidate for mersenne prime #48. ****** 

20110405, 23:05  #10  
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
2×7×13×29 Posts 
Quote:
That is until GPULL and/or Quantum computing turbocharges LL testing. 

20110406, 02:14  #11 
Dec 2010
Monticello
1795_{10} Posts 

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