20120309, 17:28  #1 
Mar 2012
Northeast US
2 Posts 
ECM on small Mersenne Numbers
I have a question about the ECM test on small Mersenne numbers. What is the purpose of finding factors of these numbers, since the entire exponent range in which ECM is being performed has already been checked by either LL or factoring? I'm guessing there must be a reason to run ECM; is finding more factors in this lower range useful in some way?

20120309, 18:19  #2  
Oct 2011
1010100111_{2} Posts 
Quote:


20120309, 18:46  #3 
Mar 2012
Northeast US
2 Posts 
OK, so it is an attempt to find all of the factors of each Mersenne number, as opposed to any factor.

20120309, 19:23  #4  
P90 years forever!
Aug 2002
Yeehaw, FL
7691_{10} Posts 
Quote:
You are right in that this does not help at all in the goal of finding new Mersenne primes. But some of us find a known factor more satisfying than a couple of matching LL results. 

20120310, 02:49  #5 
Aug 2006
3×1,993 Posts 
It is useful to have the full factorization of the first X Mersenne numbers for certain numbertheoretic algorithms. Jan Feitsma used factorizations of this type to speed his search for pseudoprimes up to 2^64, for example.

20120310, 03:47  #6  
"Richard B. Woods"
Aug 2002
Wisconsin USA
1E0C_{16} Posts 
Quote:
It is possible to do ECM on Mersennes for which a factor is already known, but it's more complicated to get PrimeNet to register an assignment in this case  one can't just simply ask PrimeNet for an ECM assignment. The procedure to follow in order to get an assignment registered in such cases is described here: http://www.mersenneforum.org/showthread.php?t=11308 

20120316, 16:31  #7 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2^{2}·11·223 Posts 
This is to report a small "misbehavior" of the server when ECM for small mersenne is reported. I did not want to create a new topic, as we have already one and it seems to be in the right subforum too.
So, I found by mistake (related to my activity in the last days, see this thread) that one can do multiple reports for the same ECM result he gets. For example, once you have a "valid" ECM result ready to be reported like this (the assignment keys made up): Code:
[Fri Mar 16 11:53:26 2012] UID: LaurV/pinch, M6620423 completed 3 ECM curves, B1=50000, B2=5000000, We4: AB3A7E78, AID: EE233FA52592387CD6D97C67F58FD73E As a sample: Code:
Manual testing 6622997 NFECM 20120316 16:26 0.0 3 curves, B1=50000, B2=5000000 0.9947 Manual testing 6622997 NFECM 20120316 15:52 0.0 3 curves, B1=50000, B2=5000000 0.9947 pinch 6622997 NFECM 20120316 13:42 5.2 3 curves, B1=50000, B2=5000000 0.8550 This is the same 3 curves, reported 3 time. I swear I did not run 9 curves :D I reported it second time by mistake, then I wanted to verify third time to check if is only maximum one manual report and one automatic report, as the credit was different, seems it is not limited, I tried the third just a minute ago, and it went on, gaving me another buck. Till morning I could go to be first in the ECM top producers :P Just FYI, maybe this is known already. Last fiddled with by LaurV on 20120316 at 16:37 
20120316, 18:12  #8 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
My guess would be that it is known, and the assumption is that only those who actually care for factors (and therefore not credit) would do ECM that doesn't help the project's initial goal, and therefore won't cheat. If someone who wouldn't do ECM otherwise does this just to inflate the credits, well, no one will die if we miss a factor.

20120316, 21:47  #9 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 
ISTM repetitious ECM result reporting will just cause PrimeNet to go to higher B1/B2 values sooner than ordinarily warranted.

20120919, 00:00  #10 
Feb 2012
110010101_{2} Posts 
Say, when doing multiple ECM curves on a single exponent; and the computer is configured for stage two only on high memory. What is there to prevent Prime95 from starting stage one of the next curve while waiting for high memory for stage two?
Is it just that this feature is not implemented, or is there a fundamental obstacle? Thanks. 
20120919, 03:19  #11 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2^{2}×11×223 Posts 
Nothing. It works like that, and that's the reason of max high workers parameter in the ini file. I discussed before if I queue P1 assignments for 30 days on 8 workers (say 200 exponents), but allow only 2 workers to stage 2, then it ends up after about 18 days with all of expos stage 1 done, few of them completed (stage 2 done), two workers doind stage 2, and .... 6 workers waiting. The discussion was where I was arguing to increase B1 manually, until you get a balance, i.e. the time needed to stage1 be about 3 times longer than the time needed for stage2. In this case (increasing B1) you increase your chances better then BRSextension, and also get bigger PrimeNet credit
You always have to work the best compromise B1/B2 for your system and expo ranges. If you have lots of memory, give it to P95 and let it chose automatically. Or use less workers, but give more cores to each worker. In this way you can max your chances without limiting the memory for stage2 too much. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Small inconsistencies between mersenne.org and mersenne.ca factor databases  GP2  mersenne.ca  44  20160619 19:29 
Use Msieve NFS for small numbers?  skan  Msieve  8  20130226 20:35 
P1 on small numbers  Unregistered  Information & Answers  2  20110822 22:53 
A new Strong Law of Small Numbers example  cheesehead  Math  7  20090206 20:49 
trial factoring of "small" mersenne numbers  antiroach  Lone Mersenne Hunters  6  20030716 23:35 