20211215, 12:01  #1  
"Lisander Viaene"
Oct 2020
Belgium
1101101_{2} Posts 
(Preying for) World Record P1!
I'd like to organize a thread to find World Record Factors with P1 on small exponents. I'll now refer to this project as WR P1 (at the risk of it sounding too pretentious, perhaps ) That would make this a subsubproject of GIMPS! Similar to Petrw1's <2k (sub twok, <twok...) project, although that name is much catchier than WR P1 in my opinion
All of these small exponents will need to be P1'ed to very high bounds. For now, it's best to only run stage 1 on these exponents (see quoted post below). However, this is where I'm stuck. The maths behind P1 escapes me. Let alone the conversion from previous ECMGMP work done to what that could equate to in terms of P1 bounds ("previously done"). Quote:
What I can do for now, however, is draft up some way of organizing this effort. Here goes nothing: I suggest we limit our effort to the 1M range for the foreseeable future. Subsequently, our current efforts should be focused on the 100k range. (Once this range has been completed, we take the next 100k range, and so on...) Within this 100k range, I'd like it to be possible to 'reserve'/claim certain ranges, with the smallest range being 1k. I'd like to reserve the 5k range (all exponents from 5000 to 6000) I'll attempt to take this range to B1=2 trillion (2,000,000,000,000 (as suggested by Zhangrc) For a bit of backstory, I realized that lots of very small exponents that have already been factored, but are not cofactor PRP, (starting from exponent M4013) never had any P1 done to date. This prompted me to find more of these exponents that never had any P1 done previously. Upon my request, James Heinrich added a checkbox to https://www.mersenne.ca/morefactors.php to find these exponents that have had no P1 done before. Though later it was pointed out that these exponents have had extensive GMPECM done, and any P1 done would have to be to very high bounds to have a crack at finding more factors. Credit to Zhangrc for coming up with the name for this project! Quote:
Last fiddled with by petrw1 on 20211218 at 04:32 

20211215, 12:03  #2 
"Lisander Viaene"
Oct 2020
Belgium
109 Posts 
Post reserved for factors found within this projects active ranges.

20211215, 12:08  #3 
"Lisander Viaene"
Oct 2020
Belgium
155_{8} Posts 
Taking George Woltman's advice, let's wait with starting stage 2 on these exponents. For now, I'd like to open up discussion on what B1 would be sufficient to take these ranges up to. Zhangrc suggested the following bound:
https://www.mersenne.ca/prob.php?exp...0&b2=1.0E%2B17 
20211215, 14:13  #4  
"University student"
May 2021
Beijing, China
11111010_{2} Posts 
Quote:
Then you assume no factor below 2^95 and let Prime95 automatically decide the B2 bounds for you. 

20211215, 14:32  #5 
P90 years forever!
Aug 2002
Yeehaw, FL
17312_{8} Posts 
I don't know if there is a "correct" B1 value. It may simply depend on how much patience you have.
FWIW, my aging quad core can compute 4 exponents around 80K to B1=300M in just under 2 hours. Extrapolating I should be able to take four 5K exponents to B1=1T in about 17 days. A pretty significant effort considering the number of exponents to work on. I'll reserve the 79000 to 82000 area for P1. I've been doing B1=300M and annoyingly this range has not given me a new factor yet. I think I'll try B1=3 to 5 billion. @James: Can the P1 probability calculator be changed to allow more than 95 bits of TF? Or even better, estimate the proper TF value given the amount of ECM that's been done? If anyone has old P1 files to donate that can be used as a starting point please let us know. We could set up a repository for future P1 efforts. 
20211215, 14:39  #6  
Jun 2003
23·233 Posts 
Try to keep the following in mind while doing large B1. Although, 2e12 seems so large that it would barely make any difference, I guess.
Quote:


20211215, 16:15  #7 
"Lisander Viaene"
Oct 2020
Belgium
109 Posts 
First off: I'm not able to keep editing my posts (mainly the first and second one in this thread), but given the nature of this thread, I'd like to request the ability to do so. It might be much easier to keep track of reservations if it's all being done in one post. Should I contact someone specifically to request this permission if it's a possibility? If not, I could set up a google sheet to keep track of reservations.
I've spread out my worktodo with exponents on each core (6 cores), B1=2T and it seems like this would take 28 days per exponent (with B1 only). There are a little more than 100 exponents (with factors found) and only three exponents with no factors found in the 5k range... B1=200B takes it down to three days and change, B1=20B takes it down to seventeen hours, B1=2B becomes two hours. I'll start out with taking all exponents in 5k to 2B, which for almost half will be the first P1 done (though this is not an accurate indicator of further factoring success ;) ) Until 30.8 (or perhaps a further version) comes along with multithreaded P1 on small exponents, I'll hold off on doing stage 2 on these exponents. Instead, further increasing B1 with every round seems like the best option for now. I might be able to muster enough patience to bring B1 up with 1 days worth of work per exponent. @axn, Do you know how the memory usage increases with a higher prime threshold? I assume it doesn't scale linearly in the sense that 500 million would become 100 MB? @Prime95 Hopefully 3B to 5B gives you some factors! As mentioned above, it might be a bit hard to keep track of reservations for a bit but I've noted you down for 79k, 80k and 81k (if I understood correctly) 
20211215, 16:59  #8  
Jun 2003
23·233 Posts 
Quote:
EDIT: Note that if you take a number to some B1, and later on increase it, it will use the slower method, Try to go directly to the largest B1 that you can comfortably do with the faster method (say, 1e10) Last fiddled with by axn on 20211215 at 17:05 

20211216, 12:32  #9 
Aug 2020
79*6581e4;3*2539e3
503 Posts 
I really like that idea, to me finding new factors of small Mersenne numbers is more interesting than factors of very large Mersenne numbers.
Why is it considered better to just do B1 at first? I there a deeper mathematical/efficiency reason for it, or is it just because new features for stage 2 will come and we want to make use of them? How exactly are stage 1 results fed to mprime? Do I just keep the files from a B1=B2 run and mprime will automatically notice when I do that exponent again with B2 > B1? 
20211216, 12:58  #10  
Jun 2003
23·233 Posts 
Quote:
Yep. 

20211216, 13:50  #11  
Aug 2020
79*6581e4;3*2539e3
503 Posts 
Quote:
Quote:
Last fiddled with by bur on 20211216 at 13:53 

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