20140215, 10:46  #34 
(loop (#_fork))
Feb 2006
Cambridge, England
2×29×109 Posts 
I think the confusion here is in the way that GMPECM interprets B2.
The available B2 are very quantised  they're roughly k * 4^n * magicconstantdependingontheinputnumber, for small integer k and n, and what you specify is a value that the B2 used must exceed. The magic constant is about 2.85 billion for numbers of up to 1920 bits. For example, Code:
echo "2^10611"  ecm v k 1 c 1 1e5 192e9 If you leave out the explicit 'k', then the actual B2 you get are Code:
97..144 k=3; B2=144.26G 145..192 k=4; B2=192.35G 193..240 k=5; B2=240.44G 241..288 k=6; B2=288.54G 289..388 k=2; B2=388.07G 389..582 k=3; B2=582.12G Last fiddled with by fivemack on 20140215 at 10:52 
20140215, 17:01  #35 
Sep 2009
5·383 Posts 

20140215, 20:29  #36  
"Curtis"
Feb 2005
Riverside, CA
2·3·733 Posts 
Quote:
See post #24 for Henry's definition of k. Since it had already been defined in this thread, I felt no need to provide context. Post #20 and 21 refer to using the I option in GMPECM to slowly increase B1 after each failed curve. I was referring to this software option with my "iterating B1 up slowly", as a reply to Walter's curiosity whether using the I option would be more efficient than the traditional method of running a set number of curves at a fixed B1 and then increasing B1 to a level optimal for a larger desired factor. You state the procedure for changing B1, B2 does not depend on implementation. But GMPECM is rather coarse in available B2 choices what if the method from your paper suggests, say, B2 = 450e9 but GMPECM only offers 388e9 and 582e9? Is it possible that a different choice of B1 with one of those available B2 values would be more efficient than your method's calculation suggests as optimal? Chris k is used by GMPECM whether you invoke the commandline option or not. We can force GMPECM to use a certain number of blocks with the k option, or allow it to choose k on its own. GMPECM only uses B2 values multiples of {list of small values I haven't studied}, 12e9, 48e9, 192e9, 768e9, etc; so a B2 choice of, say, 144e9 causes the program to use k=3 blocks of 48e9 each. You can see this parameter choice in the verbose output of GMPECM. 

20140216, 00:20  #37  
Nov 2003
2^{6}×113 Posts 
Quote:
The response curve is VERY flat in the neighborhood of the optimum. Modest changes in B1 or B2 from the optimum won't make a lot of difference. I also doubt whether the difference could ever be observed by actual trials. One would have to collect very large amounts of data to see the difference. One can also compensate for a smaller/larger than optimum B2 by a small adjustment in B1. But it isn't going to matter in practice........ 

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