20090715, 06:15  #1 
"Mark"
Feb 2003
Sydney
1000111101_{2} Posts 
P1 on small exponents
Okay, I'm after some comments and advice here, folks. I've been occasionally playing around with P1 on small exponents that were only done to low bounds. So far this looks better than ECM on these exponents. Certainly it's much better credit/day on my old P4 1.7GHz currently doing this. I'm convinced it can be better factors/day too, which is after all the main objective. For example, my latest efforts have so far yielded 9 factors from 219 attempts. I think that's a good rate  it's a little higher than I expected.*
The PrimeNet summary shows P1 assignments on small exponents (some are mine), so the future PM1S worktype is allowed for, and I wouldn't be surprised to find I'm going over ground that is already well surveyed & charted. I have a tendency to ramble on a bit, too, which I'll try to curb. Questions! What are reasonable bounds to use, when there isn't the constraint to maximize project throughput? Is is as simple as trying to maximize factors per time spent? What are "inadequate" previous bounds, to select candidates to work with? So far I've simply gone with the smallest exponents with B1 & B2 both less than a low limit like 100000. This provides lots of candidates, but eventually the lowhanging fruit will be done. Maybe estimated probability of P1 finding a factor with the previous bounds? One thing I'd like is to be able to put a Pminus1 line or similar with specified B1 & B2 in worktodo.txt to request an exponent  currently Pminus1 lines in worktodo.txt give "unsupported assignment work type", so I have to use slightlyfaked Pfactor lines to get the assignment & then change them. Maybe there's already a way? I'm constantly learning new things about the v5 server! Anyway, I'm very patient  whenever George & Scott implement PM1S will be fine. I must apologise in advance: I may not be able to respond here much for the next couple weeks, as I'll be travelling. I'll try to look in when I can get the chance, as I'm looking forward to your replies. Some details... Most of the 219 attempts I mentioned were in the 1.4M range, had been TFd to 61 bits, had P1 with B1=B2=50000, and had 6 or more ECM curves done. I chose B1=200000, B2=5000000  partly by playing with the Mersennearies P1 probability calculator, and partly because each test took the venerable P4 1.7 about an hour. * I think Murphy has invoked the Law of Small Numbers to pay me back for not bothering to dig out old results. Previously I'd done some of this manually, trying to stay ahead of the ECM assignments, and despite a couple runs of a hundred or more between factors, overall my recollection is a range of roughly 24% factored, which I was happy with. My experience with ECM has been less fortunate  after many curves, one factor. What is the probability of a factor with a single ECM curve, anyway? 
20090715, 11:27  #2  
Aug 2002
Termonfeckin, IE
2^{2}·691 Posts 
Quote:
Quote:
Last fiddled with by garo on 20090715 at 11:29 

20090715, 11:34  #3 
Aug 2002
Termonfeckin, IE
2^{2}·691 Posts 
Just a couple of additional comments.
The really low hanging fruit was picked by our forum admin several years ago. GIMPS is desperately short of people to do P1 at the leading edge of LL. A majority of exponents being LL tested are not getting project optimal P1 testing. Would you consider doing this more projectcritical work instead? I know the PIV is slow but it should get a P1 test out in 10 days. 
20090715, 17:01  #4 
P90 years forever!
Aug 2002
Yeehaw, FL
5^{2}×311 Posts 
IMO, if you enjoy finding factors do P1 on small exponents. Choose B2 as roughly 20*B1 so that it spends an equal amount of time in stage 1 and stage 2.
I'd say that P1 and doublechecking are both shorthanded. TF definitely has too many CPUs. "Do what makes the most sense" allows me to change the server's rules for handing out assignments, which I may do someday. At present, I'm inclined to let firsttime LL testers do the P1 testing that those dedicated solely to P1 don't get to. Yeah, the LL testers may not have enough memory to run stage 2, so we won't find quite as many factors. Another choice would be to divert "do what makes the most sense" machines with lots of memory to P1 halftime or fulltime  and I think P1 would still fall behind the LL testers. I'd probably define "lots of memory" as 400 or 500 MB/core. 
20090715, 17:43  #5  
Aug 2002
Ann Arbor, MI
433 Posts 
Quote:


20090716, 00:24  #6  
"Mark"
Feb 2003
Sydney
3·191 Posts 
Quote:
Originally this machine only had 512MB RAM, so P1 on large exponents was out, and I set it doing doublechecks, which was good until the 18M & 19M ranges ran out. These days, if I set it to "what make sense" the server won't give it doublechecks, as it only has 256KB L2 cache (so no exponent over 20M). So when I increased its RAM a few weeks ago, I assumed even larger FFT sizes would be no good. But it looks like the credit/day is about the same for PM1S & PM1L*. Now I'm torn between them! Thanks for the helpful replies, garo & everyone. * Credit/day for this machine is highest for TF from 2^62 to 2^64. Next best is LL tests below 20M. 

20090716, 00:31  #7 
"Mark"
Feb 2003
Sydney
3×191 Posts 
Correction and update: 13 factors from 240 attempts!
I missed 3 factorresults because they were manually submitted and showed as FECM instead of FPM1 in the results page. 
20090716, 10:21  #8 
Aug 2002
Termonfeckin, IE
5314_{8} Posts 
I moved posts related to the discussion on GIMPS's shortage of P1 testers to this thread:
http://www.mersenneforum.org/showthread.php?p=181114#post181114 Last fiddled with by garo on 20090716 at 10:24 
20090802, 12:28  #9  
Sep 2006
Odenton, MD, USA
2^{2}×41 Posts 
Quote:
Code:
UID: harlee/P4_2600, M2114467 completed P1, B1=20000, B2=260000, Wd1: 36D6140E, AID: 228B7C6B08AC54101A132C630C7727EA UID: harlee/P4_2600, M5052589 completed P1, B1=55000, B2=907500, E=6, Wd1: 82D06CAF, AID: D202551ED26816B6776F748E8C0671FF UID: harlee/P4_2600, M5052767 completed P1, B1=60000, B2=1065000, E=6, Wd1: 82C7E9FD, AID: EC2640F9F03CBCB5C85C309637D1E220 [Tue Jul 28 15:34:01 2009] 

20090802, 20:32  #10  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
Quote:
The prime95 program (and its cousin mprime) uses an algorithm for choosing B1 and B2. The algorithm always chooses a B2 that is a multiple of B1*0.25, but it does not have a hardcoded requirement of B2 = B1*20. If the algorithm chooses a multiple that is less than 20, that is only because it calculates that the optimal balance of time versus chance of finding a factor is at that multiple. Using 20 explicitly wouldn't ruin anything; it would just be a slightly suboptimal (from a GIMPS project throughput pointofview) balance of time versus chance of finding a factor.    The algorithm's "view" might be expressed as: "Consider the time difference between using B2 = B1*13 (my choice in this specific case) and using B2 = B1*20. You would have a better chance (but perhaps only very slightly better) of factoring a mersenne number by applying that difference in time toward trying to factor some other exponent than in using that time to search with B2 = B1*20 on this exponent. But it's your call, if you want to do it  just use Pminus1= and specify B1/B2 yourself." Last fiddled with by cheesehead on 20090802 at 20:37 

20090803, 00:36  #11  
"Mark"
Feb 2003
Sydney
3·191 Posts 
Quote:
As cheesehead said, it's your call what B1 & B2 you use. I prefer larger values  probably more than optimal. For example, I did some P1 on 2M exponents earlier this year mostly using B1=100000, B2=3000000. The Mersennearies P1 probability calculator is a huge help. Quote:


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