20191030, 18:27  #1 
Jun 2019
Boston, MA
3·13 Posts 
ECM probabilities and bit levels
Hi all,
I'm getting into doing more ECM work and I'm wondering  if the expected number of curves indicated for Prime95 (e.g. 280 curves at B1=50k, 640 curves at B1=250k) are run, and no factor is found, what is the probability that we can exclude a factor in that digit range? In other words, is performing the expected number of curves, the equivalent of a "no factor found" TF result for a specific bit range? Also does anybody have a rough breakdown of what bit level each B1 level corresponds to? I understand that according to this page https://www.alpertron.com.ar/ECM.HTM that for example B1 of 50000 is the 25 digits, 250000 is 30 digits, so is it just as simple as multiplying these values by ln(10)/ln(2) or ~3.3? Thanks! 
20191030, 18:53  #2 
"GIMFS"
Sep 2002
Oeiras, Portugal
2·5·157 Posts 
If you do the prescribed number of curves for a certain B1 value (say 640 for B1 = 250,000), the chance that you miss a factor smaller than the corresponding number of digits (should it exist, in the first place...) is roughly 1/e ~36%. For B1 = 250,000 that number is 30 digits. So no, getting a NFECM result is not the same as a TF "no factor found", as ECM is probabilistic whereas TF is deterministic.
As for your second question yes, it´s as simple as you stated. PS  Welcome to the ECM tribe... 
20191030, 19:00  #3 
If I May
"Chris Halsall"
Sep 2002
Barbados
2×7^{2}×113 Posts 
Just out of interest... How big are the ECM checkpoint files for the current (reasonable) "wavefront"?
I'm looking at offering Colab / Kaggle TF'ers the option of also doing CPU work in parallel  some might be interested in doing ECM. P.S. Just recovering from an unscheduled power failure... Grrr... Now have reestablish several dozen SSH sessions into servers... 
20191030, 21:11  #4  
"Dylan"
Mar 2017
1001010010_{2} Posts 
Quote:
Not at the current wavefront, but for the two ecm runs that I have (one for M55057 and one for M7777727) the files are 13868 and 1944532 bytes, respectively. There are two backups for each of them. I am not sure if the lengths depend on the B1 or B2 bounds, however. 

20191030, 21:37  #5  
"Alexander"
Nov 2008
The Alamo City
399_{16} Posts 
Quote:
Using one of my examples, I have a 51540byte checkpoint for M205759 (B1=250k), for a ratio of 3.9922:1. Last fiddled with by Happy5214 on 20191030 at 21:40 

20191030, 22:55  #6 
If I May
"Chris Halsall"
Sep 2002
Barbados
2×7^{2}×113 Posts 

20191030, 23:02  #7 
"GIMFS"
Sep 2002
Oeiras, Portugal
3042_{8} Posts 
The size of the save files is related to the size of the exponent under test (which in turn determives the size of the FFT used).
I am currently running curves on exponents in the 29xxxx range (15k FFT) and the save files are 72Kb in size. Two save files (main and backup) are used per test, although you may choose to have two backups. If you let the server decide, it will currently assign exponents in the 13 08x xxx range (672 K FFT) and the save files will grow to 3.1 MB each. 
20191030, 23:24  #8  
If I May
"Chris Halsall"
Sep 2002
Barbados
2·7^{2}·113 Posts 
Quote:
With regards to instance design, each save file would get "thrown back" to the server when it first was "noticed". It would then be up to the server to decide how many, and for how long, they would be kept. Is there an option to set the frequency of the save files? Quote:
Even ~3 MB isn't that big a deal  we have already established that Colab / Kaggle instances are in no significant way bandwidth constrained. 

20191031, 00:28  #9 
"Dylan"
Mar 2017
2×3^{3}×11 Posts 

20191031, 00:40  #10  
Jun 2019
Boston, MA
3·13 Posts 
Quote:


20191031, 00:41  #11 
If I May
"Chris Halsall"
Sep 2002
Barbados
2·7^{2}·113 Posts 

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