20050111, 22:20  #1 
Aug 2002
Termonfeckin, IE
2^{2}×691 Posts 
11 table
Code:
Size Base Index  Diff. Ratio 251 11 311  323.8 0.99 273 11 313  325.9 0.83 319 11 317  330.1 0.96 241 11 323  336.3 0.71 344 11 331  344.7 0.99 289 11 341  322.8 0.89 /11 294 11 347  361.3 0.81 294 11 349  363.4 0.8 Last fiddled with by Batalov on 20210531 at 07:20 Reason: 11,307 is done 
20051201, 17:19  #2 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
10408 curves at B1=44M on 11,239 c246. Adds 8.02467 to p45, 1.35679 to p50 and 0.20739 to p55.
Alex 
20070216, 11:55  #3  
Jun 2005
lehigh.edu
2^{10} Posts 
First on the garo 11 table!
Quote:
here's a 4th hole, and the first report of an 11 factor, p49 = 1795306125519308524148513029485573280444347858061 finishes 11, 235 C182, difficulty 195. This is also the first 2007 factor for the old_and_tired P3cluster (after none from c155c169s with difficulty under 220). If I recall, this was a degree 4, so well worth removing from the snfs list. Bruce 

20080403, 19:14  #4  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
shorter after p51 = 219716501365259540843452614863811940554249320274071 from 11, 251 C258, leaving a c208. Bruce 

20080517, 05:31  #5 
A Sunny Moo
Aug 2007
USA (GMT5)
3×2,083 Posts 
Ran 2 curves at B1=11000000, B2=30114149530 on 11,293 C300. No factors found.

20080518, 00:30  #6  
Jun 2005
lehigh.edu
10000000000_{2} Posts 
Quote:
to p45 on the complete Cunningham list some time ago, then tests to t50. More recently, working toward complete tests to 2*t50, I completed testing the Cunningham numbers at/above C300 to 2*t50. There are only a few ranges below 2*t50, with still some numbers in c251c265 that have only been tested to 1.0*p50; and the rest of c266c299.9 at/above 1.5*t50. [That's with your B1 = 11M being p45optimal; and p50optimal being B1=43M, with t50 taking some 7,700 curves, and 2*t50 representing twice that effort.] By contrast, the BMtR list is still giving up factors in p45p49; and several of the other factoring projects offer even better prospects. Of course, I might have missed something .... Bruce 

20080518, 03:36  #7  
A Sunny Moo
Aug 2007
USA (GMT5)
1100001101001_{2} Posts 
Quote:


20080518, 14:27  #8  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
with ecm reflects its nature as a random algorithm. A link on my home page reports Quote:
from the ECMNET pages. By contrast, I used just a few months of cpu time on 3 pcs to set my first record ECM factor in 2003. But, as distinct from record ECM factors, midrange ECM factors correlate well with the amount of work done. The same page reports "During November 1, 2003 to December 31, 2004 there were 122 Cunningham factors found by ECMNET, of which 42 were found by Dodson using ....". If you check the 3rd post from Garo on the "2.0" thread, you'll see that most of the curves reported in the initial files in each of the sticky threads in the "Cunningham Tables" subforum resulted from emails between myself and Bob Silverman (first), and then between myself and Rogue, which were then tabulated by Garo. It was a major effort on his part, which has provided starting points for most of the posts in this subforum. But the Tables all start from Jan 1, 2005, and no one has considered updating the curve counts to be worth the effort  even keeping the unfactored numbers up to date has been a major effort, in this case on Alex's part. The fourth, and (so far) the last post on the 2.0thread is one of my early forum posts, dated 4 July 06, which records the t45 test I was bringing to your attention in my first reply to your post. If nothing else, you'd get a flavor of what Garo and Rogue were dealing with, when they set the initial curve counts. The factors during 2004 were obtained on a cluster of P3s, and were mostly obtained from Cunningham numbers of size below 175digits. Finishing the t45 test resulted from the release of GMPECM6, a 64bit binary supplied by Torbjorn and the arrival here of a cluster of Opterons (a NFS grant for "major research instrumentation"). Finishing t50 used a new condor pc/grid, some 700 pcs. Recent work continuing on the pc/grid brought the 100 smallest Cunninghams up to 7*t50 (including all numbers below c190); the numbers from c190c233 below difficulty 250 up to 4*t50, the rest up to 3*t50; and the numbers from c234c250 up to 2*t50. The latter parts of that reflected a "lifecycle" upgrade that replaced some P4s with core2duos, bring the pc count up to 1000. Finally, many of the curves in the region above c250 I was referring to in my previous post were done on a quadcore cluster (that has since been switched over to sieving with a ggnfs binary and .poly povided by Greg; cf the msieve thread). So if you want curve counts, you get counts! The counts themselves are not considered especially interesting; but systematically raising curve counts (along with B1 bounds/default_B2) tends over time to remove the smallest factors first. If you click the "by date" link on the "quick start" page from ECMNET, you'll see that Cunningham factors below p40 no longer appeared; then that factors below p45 became rarer; and the most recent 30 factors show that it's more likely to find a factor of 60digits or more than to find a factor below 50digits. (At least until the most recent quadcore factors from numbers above c250.) Bruce 

20080518, 23:02  #9 
A Sunny Moo
Aug 2007
USA (GMT5)
1869_{16} Posts 
Ah, I see. Yes, I knew that ECM finds factors in a random way, but I had always thought that there was an "optimal number of curves" to do at a certain B1 value before moving on to the next level. Thanks for the explanation, though!

20080519, 12:08  #10  
Nov 2003
2^{2}×5×373 Posts 
Quote:
There is. Nothing Bruce said contradicted this. You need to read my joint paper with Sam Wagstaff Jr: "A Practical Analysis of the Elliptic Curve Factoring Algorithm" in Math. Comp. It discusses two different optimizations. (1) How to select parameters when you are going to spend a *fixed* amount of time. (2) How to select parameters to maximize the probability of success per unit time spent. 

20080519, 12:31  #11  
Jun 2005
lehigh.edu
2^{10} Posts 
Quote:
was flawed here. There were a bunch of smallish factors from my run towards a 2nd t50 on the c251c384 Cunninghams; but even those were more likely to be p5x than p4x. The link I was referring to is http://www.loria.fr/~zimmerma/cgibin/last.cgi?date which lists 767 Cunningham factors reported to the ECMNET page since Jan 1, 2000. Nov 1, 2003 is at #354; which is where the count of factors from the P3 cluster started (iirc). The last 30 reports (which included most of the least tested range) is #738#767 of which there are two factors below p50 (both p48s) and two factors above p59.99 (p62 and p66), the rest p5x's. Looks like I was recalling a somewhat earlier stretch, which included the p60 at #735, but not the p48 at #731. So the claim that there were "more p6x's than p4x's" is correct for a range of 30 factors starting after #731, which gives 3to2, with the other 25 being p5x's. Checking the Cunningham site of recent factors (all methods), page 108 has the five most recent ECMNET/Dodson factors; two from the tail end of the 3rd t50 on c190c234; two from the quadcore run on c251c279 (with c266c279 complete to 1.5*t50, the +0.5*t50 only partial on c251c265) and the most recent p57 from the current Childers/Dodson number. Checking the previous page 107 fills in the two most recent p48s at #5587 and #5592 (in Sam's numbering) and the last three ECMNET/Dodson factors were all from c266c299. Hmm. So the most recent 30 (as distinct from a somewhat earlier "most recent" 30) reflects two recent p48s, and bunches of small p5xs, with no quadcore p6x. Anyway. It's clear that the p45optimal B1 = 11M is not the most likely place to look. By contrast, the current #1 on the top10 of 2008 was found by PaulZ, a p66 with p50optimal B1=43M; but I'd bet that the number of curves was in 5digits, maybe 6digits. Bruce Last fiddled with by bdodson on 20080519 at 12:41 Reason: uhm, so my recollection _was_ correct; "at least until" 

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