mersenneforum.org P-1 on small exponents
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2009-07-15, 11:27   #2
garo

Aug 2002
Termonfeckin, IE

22·691 Posts

Quote:
 What are reasonable bounds to use, when there isn't the constraint to maximize project throughput? Is it as simple as trying to maximize factors per time spent?
If your objective is to find factors, I would say yes this would be the way to go.

Quote:
 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 low-hanging fruit will be done. Maybe estimated probability of P-1 finding a factor with the previous bounds?
Yes. Use the excellent mersennaries calculator to calculate automatic bounds and choose exponents that are below the 1 or 2 test bounds - your choice. I wouldn't bother doing P-1 on exponents where the test already performed had a chance of finding a factor greater than 50% of the chance of the test using bounds you are going to use.

Last fiddled with by garo on 2009-07-15 at 11:29

 2009-07-15, 11:34 #3 garo     Aug 2002 Termonfeckin, IE 22·691 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 P-1 at the leading edge of LL. A majority of exponents being LL tested are not getting project optimal P-1 testing. Would you consider doing this more project-critical work instead? I know the P-IV is slow but it should get a P-1 test out in 10 days.
 2009-07-15, 17:01 #4 Prime95 P90 years forever!     Aug 2002 Yeehaw, FL 52×311 Posts IMO, if you enjoy finding factors do P-1 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 P-1 and double-checking are both short-handed. 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 first-time LL testers do the P-1 testing that those dedicated solely to P-1 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 P-1 half-time or full-time -- and I think P-1 would still fall behind the LL testers. I'd probably define "lots of memory" as 400 or 500 MB/core.
2009-07-15, 17:43   #5
Kevin

Aug 2002
Ann Arbor, MI

433 Posts

Quote:
 Originally Posted by garo GIMPS is desperately short of people to do P-1 at the leading edge of LL. A majority of exponents being LL tested are not getting project optimal P-1 testing. Would you consider doing this more project-critical work instead? I know the P-IV is slow but it should get a P-1 test out in 10 days.
My 2.0GHZ PIV can kick out a P-1 test in a little under 4 days, so I'd expect something closer to 6 days.

2009-07-16, 00:24   #6
markr

"Mark"
Feb 2003
Sydney

3·191 Posts

Quote:
 Originally Posted by garo GIMPS is desperately short of people to do P-1 at the leading edge of LL. A majority of exponents being LL tested are not getting project optimal P-1 testing. Would you consider doing this more project-critical work instead? I know the P-IV is slow but it should get a P-1 test out in 10 days.
Just over 6 days (Kevin's estimate was spot on); I've given it one to see how long it takes in practice.

Originally this machine only had 512MB RAM, so P-1 on large exponents was out, and I set it doing double-checks, 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 double-checks, 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 PM1-S & PM1-L*. 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.

 2009-07-16, 00:31 #7 markr     "Mark" Feb 2003 Sydney 3×191 Posts Correction and update: 13 factors from 240 attempts! I missed 3 factor-results because they were manually submitted and showed as F-ECM instead of F-PM1 in the results page.
 2009-07-16, 10:21 #8 garo     Aug 2002 Termonfeckin, IE 53148 Posts I moved posts related to the discussion on GIMPS's shortage of P-1 testers to this thread: http://www.mersenneforum.org/showthread.php?p=181114#post181114 Last fiddled with by garo on 2009-07-16 at 10:24
2009-08-02, 12:28   #9
harlee

Sep 2006
Odenton, MD, USA

22×41 Posts

Quote:
 Originally Posted by Prime95 IMO, if you enjoy finding factors do P-1 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 doing P-1 work in the 2M and some in the 5M range with 25.11 and noticed a couple of things. First, for 2M exponents, the B2 is B1*13 and for 5M exponents it is B1*16.5 then B1*17.5. Why isn't it B1*20 like Prime95 suggested?

Code:
UID: harlee/P4_2600, M2114467 completed P-1, B1=20000, B2=260000, Wd1: 36D6140E, AID: 228B7C6B08AC54101A132C630C7727EA
UID: harlee/P4_2600, M5052589 completed P-1, B1=55000, B2=907500, E=6, Wd1: 82D06CAF, AID: D202551ED26816B6776F748E8C0671FF
UID: harlee/P4_2600, M5052767 completed P-1, B1=60000, B2=1065000, E=6, Wd1: 82C7E9FD, AID: EC2640F9F03CBCB5C85C309637D1E220
[Tue Jul 28 15:34:01 2009]
Second, I seem to recall reading the output E=6 has a special meaning, can't seem to find it. Anyway, probably due to the small B1 & B2 settings the 2M exponents are not getting that by default. The is plenty of memory allocated for P-1 stage 2 (1.5GB) to use so that isn't an issue.

2009-08-02, 20:32   #10

"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×641 Posts

Quote:
 Originally Posted by harlee First, for 2M exponents, the B2 is B1*13 and for 5M exponents it is B1*16.5 then B1*17.5. Why isn't it B1*20 like Prime95 suggested?
Prime95's suggestion was a rule-of-thumb general recommendation that will give good results.

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 hard-coded 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 point-of-view) 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 2009-08-02 at 20:37

2009-08-03, 00:36   #11
markr

"Mark"
Feb 2003
Sydney

3·191 Posts

Quote:
 Originally Posted by harlee First, for 2M exponents, the B2 is B1*13 and for 5M exponents it is B1*16.5 then B1*17.5. Why isn't it B1*20 like Prime95 suggested?
It seems to be a rule of thumb. The optimum is not very peaked - you don't lose much if you move a small distance from it. Also I think it varies with the size of the exponent and the size of B1 & B2 relative to it. Hence "roughly 20".

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 P-1 on 2M exponents earlier this year mostly using B1=100000, B2=3000000. The Mersenne-aries P-1 probability calculator is a huge help.

Quote:
 Originally Posted by harlee Second, I seem to recall reading the output E=6 has a special meaning, can't seem to find it. Anyway, probably due to the small B1 & B2 settings the 2M exponents are not getting that by default. The is plenty of memory allocated for P-1 stage 2 (1.5GB) to use so that isn't an issue.
The E=6 is from something called the Brent-Suyama extension. This thread is helpful.

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