On Saturday 09 November 2002 04:45, you wrote: > > A harder problem is finding some smooth ECM curves to test. I do not > have tools to compute group orders.
Nor do I. > If someone can help by finding a > couple of dozen smooth ECM test cases for exponents between 1000 > and 500000, I would be most grateful. > If you take some examples of known factors around 2^64 in size (say 19 or 20 digits), you would _expect_ to be able to find some of these factors by running a few score "random" ECM curves with B1=100,000 & automatic B2. With luck some might even drop out in stage 1. These should yield your test cases - obviously what you need is a specific "sigma" which should yield a factor with given limits, and a specific "sigma" which shouldn't - and the second is all to easy to find! Once we have some examples, a bit of experimenting with limits should furnish the critical limits for these particular examples. I believe that calculating the group order is rather time-consuming, even with the appropriate tools, so with reasonably small factors this experimental approach might not be too wasteful. I wouldn't worry too much about covering the whole range of exponent sizes, or B limits - though those of us who have been running ECM can furnish working sigma values for specific factors we have found with large limits. The point with exponent sizes is that the code for the various FFT run lengths should already be "tested" through the "short LL residual" data set. The problems that we want to test out are those specific to the ECM stage 1 & stage 2 algorithms (and the GCD, though that should be covered with P-1). We should also be finding working examples for ECM on 2^n+1. Does this sound reasonable? If so I could pick a few suitable factors & start trying to find sigma & B limits for test curves using ECM in v22.12. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
