20170826, 23:42  #1 
Random Account
Aug 2009
3634_{8} Posts 
ECM's Repeating?
In the image attached, there appears to be repeating of ECM factoring. All have the same bounds and the same number of curves. The TF depths increase, however there is no parameter in a worktodo entry that indicates how far an exponent has been factored.
Sample: Code:
ECM2=1,2,<exp>,1,50000,5000000,3 
20170827, 00:12  #2  
Sep 2003
101000011000_{2} Posts 
Quote:
Although there does eventually come a point where you've carpetbombed the dartboard and it turns out it (almost certainly) doesn't have a bullseye, so then you might start throwing at a more distant dartboard and hope that one does have a bullseye. The more distant the dartboard, though, the more darts you have to throw to make sure you have saturation coverage, and the more effort it takes to throw them. So maybe you give up instead. TF, on the other hand, is deterministic. If you search to a given bitdepth, then you either find a factor or you don't, and there's no sense duplicating the same search twice. Same with Pβ1 by the way: it makes no sense to repeat a Pβ1 test with the same B1 and B2 parameters. Last fiddled with by GP2 on 20170827 at 00:32 Reason: added "almost certainly" 

20170827, 00:30  #3  
Random Account
Aug 2009
2^{2}×487 Posts 
Quote:


20170827, 14:45  #4 
Romulan Interpreter
Jun 2011
Thailand
2^{2}×2,381 Posts 
Additionally to what GP2 (in a very nice metaphor) said, yes, ECM starts with a "random seed" which makes the probability of two people doubling the same work very low, and you can look to this report, to have an idea about the limits and the number of curves needed at each level.
For example (see the tables), if you do about 4700 curves with B1=3M, this leaves an extremely low probability (close to zero) that a factor of 40 digits remained undiscovered. Sometimes they do indeed remain hidden (depending on their ECM "smoothness") and they are found much later, at higher bounds, or at NFS, etc (like when we factor aliquot sequences) and then we talk about an "ECM miss". But that is another story... Last fiddled with by LaurV on 20170827 at 14:51 
20170827, 16:24  #5  
Random Account
Aug 2009
2^{2}·487 Posts 
Quote:
Thank you for the report link. I will study it in more detail. 

20170827, 18:44  #6 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10,723 Posts 
I'm too lazy to compute a precise figure for the probability you describe but a quick mental calculation suggests that it's around 10%. Whether thas is "extremely low" and "close to zero" is a value judgement.

20170827, 22:33  #7  
Einyen
Dec 2003
Denmark
3^{2}·349 Posts 
Quote:
This way of doing ECM is supposedly the optimal way of searching for factors from that paper on ECM bounds that RDS coauthored and always referred to. Last fiddled with by ATH on 20170827 at 22:35 

20170827, 22:58  #8  
Aug 2006
3×1,993 Posts 
Quote:


20170831, 14:45  #9 
Romulan Interpreter
Jun 2011
Thailand
2^{2}·2,381 Posts 
That is right, I stand corrected. What I was thinking is that as you go higher and higher, your "chances" to miss factors of a specified size gets asymptotically lower and lower...
Anyhow, the man got the idea... 
20171111, 01:08  #10 
Random Account
Aug 2009
2^{2}·487 Posts 
I have noticed after running ECM's for a while that the bounds in the worktodo file always seem to be the same: B1=50000, B2=5000000. This holds regardless of the size of the exponent. Is this a constant, or does Prime95 change this as it runs?
There is also a relationship between the RAM allocation and the size of the exponents assigned. This, I understand. However, if I go beyond 2560M, I start seeing pauses in Stage 2 with some as long as 20 seconds. The CPU load does not decrease during this time. Perhaps I am limited because of the total RAM in this machine, 8GB. I have been meaning to increase it to 16GB, but never seem to get around to getting it done. 
20171111, 10:08  #11 
Feb 2016
! North_America
1010000_{2} Posts 
Are you assigning it with https://www.mersenne.org/manual_assignment/ ? It should give you the corrent B1 B2 in the assigment (just tried out with a 10k number), and you can manually edit the number of curves in the worktodo. Possibly (maybe) the bounds too.
https://www.mersenne.org/report_ecm/ second table as other commenters pointed out. It's giving you the column which isn't done. Last fiddled with by thyw on 20171111 at 10:09 
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