20220920, 08:53  #12 
"Martin Hopf"
Jul 2022
Germany
42_{10} Posts 
To enlighten the mystery a bit.
The group order can be determined with Suyama's parametrization iff the factor was found in stage 1.
go.gp Code:
go(p,sig) = { /* group order with Suyama's parametrization */ local(u, v, x, z, An, Ad, A, b, E); u = sig^25; v = 4*sig; x = u^3; z = v^3; An = (vu)^3*(3*u+v); Ad = 4*x*v; A = An/Ad2; b = (x^3+A*x^2*z+x*z^2)/z; E = ellinit([0, b*A, 0, b^2, 0]); ellcard(E, p) }; Code:
================================================================================ ECM on 6^16384+1: curve #223 with s=7941809365880582, B1=50000, B2=50000 6^16384+1 has a factor: 18220289247208144897 (ECM curve 223, B1=50000, B2=50000) factor(go(p, sig))~ %1 = [2 3 17 523 719 1097 1153 23473] [5 1 1 1 1 1 1 1] ================================================================================ ECM on M5113: curve #45 with s=3943578567805877, B1=50000, B2=50000 M5113 has a factor: 44652248830618077673 (ECM curve 45, B1=50000, B2=50000) factor(go(p, sig))~ %2 = [2 3 13 1181 13691 27397 35897] [3 3 1 1 1 1 1] ================================================================================ ECM on M8069: curve #28 with s=8417003857061369, B1=50000, B2=50000 M8069 has a factor: 3133683643066645087 (ECM curve 28, B1=50000, B2=50000) factor(go(p, sig))~ %3 = [2 3 19 1201 4783 6869 29027] [4 2 1 1 1 1 1] ================================================================================ 
20220921, 19:47  #13 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{3}×1,019 Posts 
The bad sigma problem just happened to me, so it was not a onetime memory corruption  it is a prime95 bug.
The most concerning thing is that the factor is not found by prime95 when rerun with the same sigma. It would be a minor problem if prime95 was computing curve starting parameters from a sigma value differently than GMPECM and other programs. I think it is a major problem that prime95 sometimes finds a factor with a given sigma and sometimes does not. Studying the code, I'm presently at a loss as to where the problem might be. 
20220921, 23:47  #14 
Mar 2006
2^{2}·7·19 Posts 
Is there any way we can see the code for this new ecm functionality? Perhaps an extra pair of eyes, or a dozen!, can help find any potential issues.

20220922, 05:26  #15 
Einyen
Dec 2003
Denmark
2×17×101 Posts 
Is it only a problem in the new version 30.9 ECM or also older versions?

20220922, 06:18  #16 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{3}·1,019 Posts 

20220922, 15:56  #17  
Sep 2009
5^{2}×97 Posts 
Quote:
Or is there any other pattern to when it works and when it does not? Does *always* work or not when run in *exactly* the same way? 

20220922, 17:07  #18 
Jun 2003
2^{2}×3^{2}×151 Posts 

20220922, 17:41  #19  
P90 years forever!
Aug 2002
Yeehaw, FL
2^{3}·1,019 Posts 
Quote:
I've only tried rerunning the found factor twice. It failed to find the factor both times. I cannot yet explain how this could happen  you're right it smells like some kind of improperly initialized variable. Quote:
The person that reported the original problem came up with the breakthrough to finding the bug. He used GmpECMHook=1 to dump the output of ECM stage 1. He found that version 29.1 and 30.9 produced different results. I've narrowed the change down to versions 30.5 and 30.6. Now I have to go through source control and apply changes one by one to find the exact change that caused the difference. 

20220922, 18:13  #20 
Einyen
Dec 2003
Denmark
2×17×101 Posts 
Do you have the entire log? Did you try run all 4 curves again using the same 4 different sigmas?

20220922, 19:53  #21  
P90 years forever!
Aug 2002
Yeehaw, FL
1FD8_{16} Posts 
Quote:


20220922, 20:33  #22 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{3}×1,019 Posts 
I've created a special version that always dumps the stage 1 result. I'm searching again for new factors in hopes the problem comes up again. At least then I'll be able to tell if the problem is from stage 1 or stage 2.
My best guess is some kind of multithreading bug in stage 2 (hence nonreproducible) where the bad result luckily stumbles upon a factor. Though, that seems almost unbelievably lucky.  Edit: Even better, I now dump stage 1 and stage 2 result. I'll run several curves and then rerun them again withe same sigmas and compare results. Last fiddled with by Prime95 on 20220922 at 21:02 
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