mersenneforum.org > Data P-1 / P+1 / ECM strategy for PRP-CF
 Register FAQ Search Today's Posts Mark Forums Read

 2021-05-03, 19:37 #56 alpertron     Aug 2002 Buenos Aires, Argentina 25148 Posts In 2015 I ran the P-1 algorithm for all exponents between 0.0M to 2.8M with a known factor with B1 = 500K, B2 = 15M. Unfortunately at that time the server rejected manual results if no factors were found. I uploaded many of the results when the server started to accept these results. Unfortunately there were many results.txt files that were lost. So probably that's why some ranges show zero attempts of P-1.
2021-05-03, 19:51   #57
pinhodecarlos

"Carlos Pinho"
Oct 2011
Milton Keynes, UK

10011001111102 Posts

Quote:
 Originally Posted by masser Please see attached. After reading comments above, I adjusted TF level to 77. Let me know if you need something different.

Thank you. It's running.

 2021-05-03, 20:21 #58 masser     Jul 2003 wear a mask 32·179 Posts Questions about P+1 Strategy Let's assume I dedicate G ghz-days of computational effort to run a P+1 curve on a Mersenne number. When I do this, mprime/prime95 reports a probability of finding a factor as X%. If I then repeat another P+1 curve on the same exponent, with the same effort, bounds, but a different starting seed, will my probability of finding a factor now drop to X/2%? (I know the software will continue to report X%). If I were to complete three P+1 curves on the save exponent, each with the same effort and bounds, but different starting seeds(nth_run = 1,2,3), will my total probability of finding a factor be 7X/4 = (1+1/2+1/4)X? Does it make more sense to do one curve with 3G of computational effort or 3 curves with different starting seeds, each with G level of computational effort? It's hard to imagine a case where the Probability increases by a factor of 7/4 when the effort increases by a factor of 3, but I'm uncertain of how the probabilities work with P+1 curves. Last fiddled with by masser on 2021-05-03 at 20:23
2021-05-03, 21:12   #59
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

22·1,873 Posts

Quote:
 Originally Posted by masser If I then repeat another P+1 curve on the same exponent, with the same effort, bounds, but a different starting seed, will my probability of finding a factor now drop to X/2%? (I know the software will continue to report X%).
Close to X/2%. Peter Montgomery says the 6/5 seed is not quite as productive as the 2/7 seed. Prime95 reports the slightly-less-than-X/2% number. That is, prime95 assumes using nth_run=2, you ran P+1 with the same B1/B2 with nth_run=1.

Quote:
 If I were to complete three P+1 curves on the save exponent, each with the same effort and bounds, but different starting seeds(nth_run = 1,2,3), will my total probability of finding a factor be 7X/4 = (1+1/2+1/4)X?
Again, slightly less.

Quote:
 Does it make more sense to do one curve with 3G of computational effort or 3 curves with different starting seeds, each with G level of computational effort?
You'd have to run some tests. My gut instinct says that nth_run=3 would not be profitable. That is do two runs at 1.5G effort. I have no data to back up this hunch.

2021-05-04, 02:22   #60
Happy5214

"Alexander"
Nov 2008
The Alamo City

10010111012 Posts

Quote:
 Originally Posted by keisentraut So, please give it a try :) All you need to do is to install Python, download it from github and then run "python.exe get_work.py 123000 124000". Here is an example of it in work.
Your shebang (line 1) is wrong. Linux distros (well, at least Ubuntu) name their Python 3 interpreters /usr/bin/python3 (/usr/bin/python is always Python 2), so that script will not run unmodified with the executable bit set.

2021-05-04, 09:37   #61
keisentraut

Jul 2020

23 Posts

Quote:
 Originally Posted by Happy5214 /usr/bin/python is always Python 2)
My favorite distro switched it 10+ years ago :) But you are right, I changed it a few hours ago.
The most controversial thing about my script is probably that my script increases the desired P+1 bound to half of P-1 if there is a very large run of P-1. For a few exponents this might result in surprisingly "heavy" assignments but I think P-1 B1 / P+1 B1 ratio should be approximately constant and if the P+1 is only done too a low bound then this results only in having to redo it in the long term.

2021-05-04, 17:07   #62
masser

Jul 2003

32·179 Posts

Quote:
 Originally Posted by Prime95 You'd have to run some tests. My gut instinct says that nth_run=3 would not be profitable. That is do two runs at 1.5G effort. I have no data to back up this hunch.
Thanks for the feedback - it's very helpful. I'm collecting some run times and probabilities, and I will have a few more questions later, but your hunch appears to be correct.

Here are the probabilities reported by v30.6b4, for an exponent in the 14.03M range, TFed to 72 bits, with B1 = 900K.

nth_run = 1: Prob = 0.68%
nth_run = 2: Prob = 0.318%
nth_run = 3: Prob = 0.0713%

The drop in probability from nth_run = 2 to 3 seems too severe. Is that correct?

2021-05-04, 23:52   #63
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

11101010001002 Posts

Quote:
 Originally Posted by masser nth_run = 3: Prob = 0.0713% The drop in probability from nth_run = 2 to 3 seems too severe. Is that correct?
I think that's right, but I'd appreciate confirmation from the math experts.
nth_run=1 finds all 5 mod 6 smooth factors
nth_run=2 finds all 3 mod 4 smooth factors (that aren't 5 mod 6)
nth_run=3 finds one-half of the smooth factors that aren't 3 mod 4 or 5 mod.

The reason for a factor of 4 rather than the expected factor of 2 is we lose one "free bit" of smoothness. With nth_run=2 our "search space" is 3 mod 4 factors, with nth_run=3 we've doubled our "search space" factors that are 1 or 3 mod 4.

2021-05-05, 18:55   #64
pinhodecarlos

"Carlos Pinho"
Oct 2011
Milton Keynes, UK

114768 Posts

Quote:
 Originally Posted by pinhodecarlos Thank you. It's running.
Done.

2021-05-05, 19:09   #65
masser

Jul 2003

31138 Posts

Quote:
 Originally Posted by pinhodecarlos Done.
More? Longer tasks/higher bounds? Different range?

2021-05-05, 19:36   #66
Prime95
P90 years forever!

Aug 2002
Yeehaw, FL

22×1,873 Posts

Quote:
 Originally Posted by Prime95 Continuing on. Now doing 312500 to 314000 (exponents with known factors)..
Continuing on to 314K doing P-1 using the keisentraut Python script.

This has hardly been the factoring bonanza I was hoping for -- 165 consecutive failures. I'm beginning to wonder if this area has already had deep P-1 run but not reported to the server (or was done before the server accepted P-1 results on factored exponents).

Last fiddled with by Prime95 on 2021-05-05 at 19:36

 Similar Threads Thread Thread Starter Forum Replies Last Post Prime95 PrimeNet 103 2012-04-09 07:39 davieddy Lounge 34 2012-03-17 02:03 diamonddave GPU to 72 18 2011-12-06 19:56 Kees Puzzles 4 2006-04-07 07:17 Citrix Prime Sierpinski Project 5 2004-10-31 12:25

All times are UTC. The time now is 05:18.

Fri May 14 05:18:07 UTC 2021 up 35 days, 23:58, 0 users, load averages: 1.69, 1.63, 1.67

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.