20180505, 12:49  #1 
Oct 2007
Manchester, UK
2×3×223 Posts 
Odd behaviour in ECM with p95 v29.4
As a lark I decided to do some ECM on an unreasonably large number, which has some known factors already; 3^5198+1
I remember that Prime95 seems to be faster at stage 1 than GMPECM, so I decided to try it for this. From the documentation, it is possible to set up ECM in the worktodo.txt file as follows: Code:
ECM2=k,b,n,c,B1,B2,curves_to_run[,"commaseparatedlistofknownfactors"] Firstly, Prime95 seems to either crash or enter an infinite loop if I jam all of the known factors together, such as this: Code:
ECM2=1,3,5198,1,1000000,1000000,1000,39144695176586244470086916951706412096252695690001050295503066390090860724430123140913783684262335502958184703622641033499578807467353838957246838778730 But the second issue is that even when I give the prime factors individually, they seem to be ignored. As a test I ran this: Code:
ECM2=1,3,5198,1,11000,11000,100,2 As a user I would like to be able to supply all known factors, then have it divide them out and run ECM on the remainder. Or better yet if there were simply a way to directly input the number I want to run ECM on, insted of requiring it be representable as k*b^n+c first. Reporting already known factors seems like unexpected behaviour, and in this case prevents me from running ECM at all, as it is overwhelmingly likely to find one of the small factors then stop. If it matters, I am running this on Windows 7 on a Haswell CPU with the FMA3 FFT. 
20180505, 12:54  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×31×97 Posts 

20180505, 12:55  #3 
Oct 2007
Manchester, UK
2×3×223 Posts 
I believe the same issue occurs when using large numbers as inputs here too.
Edit: But please tell me what you believe 0^0 is. Edit 2: I ran a quick test on this (with n=1), and c = c2329. The result was, "Cannot initialize FFT code, errcode=1003" Last fiddled with by lavalamp on 20180505 at 12:59 
20180505, 13:04  #4  
Dec 2016
5·11 Posts 
Quote:
Code:
ECM2=1,3,5198,1,1000000,1000000,1000,"39144695176586244470086916951706412096252695690001050295503066390090860724430123140913783684262335502958184703622641033499578807467353838957246838778730" 

20180505, 13:10  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
13576_{8} Posts 

20180505, 14:50  #6  
Oct 2007
Manchester, UK
2×3×223 Posts 
Quote:
Edit: Correction, it didn't crash it, but it temporarily wiped all text from the worker window, but then started running again. Albeit very slowly. I will investigate further. Edit 2: OK, that seems to work now. I think the PC was a bit overloaded with some other work. Last fiddled with by lavalamp on 20180505 at 14:55 

20180506, 03:24  #7  
Jun 2003
37×131 Posts 
Quote:
Code:
ECM2=1,3,5198,1,1000000,1000000,1000,"2,5,2713,12553493,18495731521,3536878321177,70601370627701,798087896392921,31181934032520084217683832052280453426721598216094871026492932287412448715951254226575121" The whole point of using P95 is that it can run k*b^n+/c numbers very efficiently. If the number is not of that form, you might as well use GMPECM for stage1, because it wouldn't be run efficiently by P95 (assuming it can run it at all  I dont think P95 supports arbitrary numbers). 

20180506, 05:14  #8  
Oct 2007
Manchester, UK
10100111010_{2} Posts 
Quote:
If the k*b^n+c form is faster for ECM, then would it make sense to search for representations of general numbers in that form, akin to searching for polynomials in GNFS? Although I can see the value for c becoming quite large. 

20180506, 17:08  #9  
Jun 2003
37×131 Posts 
Quote:
Only a very small fraction of numbers can be represented using the k*b^n+c form (assuming some restriction on the sizes of each of those constants). Let's say that k,b,n,c all are restricted to be at most 64 bits. Then there are only 256 bits worth of numbers that we can represent. It is highly unlikely that we can find a viable (k,b,n,c) represenation for an arbitrary number so that it can be handled by P95. 

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