20181205, 21:18  #34  
Sep 2003
2589_{10} Posts 
Quote:
There are still new factors being found by ECM on a regular basis. If you are interested in finding any new factors, including second and higher factors of exponents which already have at least one known factor, then it's probably a tossup whether you choose small or large Mersenne numbers. If you're mostly interested in finding first factors of exponents without any known factors, then I think it is easier to find them for larger Mersenne numbers, simply because there's a lot of unexplored territory. 

20181205, 21:29  #35  
"Curtis"
Feb 2005
Riverside, CA
2·2,819 Posts 
Quote:
However, the probability of 1 ECM curve finding a factor for a number depends heavily on how much previous ECM has been run; if the ECM size you're considering has already been run thousands of times, the chances of the next one finding a factor are quite small compared to chances of the first ECM curve run on a number! In terms of probability of finding a factor per day..... that's complicated. Smaller numbers have already been ECM'ed to small and medium bounds, so you'll need to use a pretty big ECM curve to find a factor; however, since the input is small, this curve might take a similar amount of time as smaller B1/B2 bounds on larger inputs. I think GP2 was commenting on this "factors per day" probability in his reply. Last fiddled with by VBCurtis on 20181205 at 21:30 

20181205, 21:38  #36  
"6800 descendent"
Feb 2005
Colorado
1011100011_{2} Posts 
Quote:
The numbers I'm being assigned are in the M12,000,000 and M19,000,000 range, with 4096MB of memory assigned (prime95 is actually using 3808MB in stage 2). From what I can tell, all the numbers I'm getting have never had any curves run on them. So, based on your input, on numbers that have no prior curves run, the probability of any 1 curve finding a factor is not dependent on the length of the number being factored. 

20181205, 21:58  #37  
If I May
"Chris Halsall"
Sep 2002
Barbados
3×5×739 Posts 
Quote:
Flip a fair coin a thousand times and it turns up heads each time. What is the chance it will turn up tails the next flip? 

20181205, 22:42  #38  
"6800 descendent"
Feb 2005
Colorado
739 Posts 
Quote:
That is why I am running only 1 curve per candidate, and I assumed it is why the server assigns curves this way. So if I hammer one number with 100 or more curves, and that number happens to have only a few very large, almost equal factors, the chances of finding them is almost zero. All those curves would be wasted. However, if I run just one curve per number, some of them will be run on numbers with lots of factors, which decreases the chance of wasting curves on impossible candidates. Of course I may be way off base here, because I admit the math is way above my head. Last fiddled with by PhilF on 20181205 at 22:47 

20181205, 22:52  #39  
Nov 2008
509 Posts 
Quote:
ECM found a factor in curve #25, stage #2 Sigma=3673943552503015, B1=1000000, B2=1000000000. UID: nitro/haswell, M85027 has a factor: 113574028377227867558212550573836752813871 (ECM curve 25, B1=1000000, B2=1000000000) 

20181205, 22:53  #40 
If I May
"Chris Halsall"
Sep 2002
Barbados
3·5·739 Posts 

20181205, 23:03  #41 
Nov 2008
111111101_{2} Posts 
How much ram will it use?
I am referring now to gmpecm.
I'm currently working on M4007 with fairly high values for B1,B2 B1=32X10^{11} B2=12x10^{14} I have 32gb in this system and gmpecm will try to use all that it can, there is a bug either in gmpecm or windows memory management. When it gets to 16gig (not a typo) and tries to allocate another 4 gig chunk it fails with out of memory  even though 8 gig is still free...so I cap it at 14 gb for stage 2 
20181205, 23:54  #42  
"6800 descendent"
Feb 2005
Colorado
739 Posts 
Quote:
I was under the impression that the reason the curves are split up into "levels" is due to the very reason I spelled out. Once a sufficient number of curves have been run at a specific level of a specific number, that level is considered done and the next level started. That is because the chance of finding a factor goes down as each curve in a level is run. Am I wrong? Last fiddled with by PhilF on 20181205 at 23:58 

20181206, 00:08  #43 
If I May
"Chris Halsall"
Sep 2002
Barbados
3×5×739 Posts 

20181206, 02:07  #44 
Random Account
Aug 2009
Not U. + S.A.
9E5_{16} Posts 
All of this is based on using random numbers. One could never be certain that all of the existing factors could be found at any level. I suppose the word "done" could be applied if many thousands of CPU's did many thousands of curves and found nothing new. Still, the possibility remains.

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