mersenneforum.org Introduction: ECM work done on Cunningham Project composites
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2005-01-11, 22:08   #1
garo

Aug 2002
Termonfeckin, IE

22·691 Posts
Introduction: ECM work done on Cunningham Project composites

In this subforum we are attempting to summarize the amount of ECM work
known to have been done on the Cunningham Table composites.

Several changes have been introduced from version 2.0. Hence the description below in quotes is not accurate anymore. I am leaving this in only for record-keeping purposes. please read the new introduction at:http://www.mersenneforum.org/showthread.php?p=58344
Quote:
 Originally Posted by v1.0 At this point we are creating 16 threads, two for each base, + and -. The LM tables are included in the appropriate + or - table. I will be putting up an FAQ post with information on what LM stands for, what are Cunningham tables and other questions later this week. The precise figures in these tables are almost certainly incorrect, not least because many researchers haven't reported how much work they have completed. Another important source of error is that different runs of different ECM programs may use different values for the stage 1 and stage 2 bounds B1 and B2. We take a very conservative estimate, so the tables indicate the minimum known to be done. That said, we believe that the figures are correct enough to be useful and where we err the figures we give will indicate that more work needs to be done and not less than is in fact the case. In particular, we assume that the B1 values are as given in each table heading (11M, 43M, 110M, 260M) to seek factors of (45, 50, 55, 60) decimal digits respectively and that in each case B2=100*B1. In addition to the number of prime95 equivalent curves we also indicate the proportion of work that has been done. So a (1.0) in paranthesis signifies that the optimal number of curves have been run at that level. A number less than 1.0 indicates more effort at that level is required and use NR (= Not Required) to indicate when no more curves need to be run at a particular level even if the number of curves run is less than optimal. This is because running curves at higher B1 levels reduce the chances of finding a smaller factor making running curves at smaller B1 less useful. We would appreciate learning of any errors in, and updates to, these tables. Please send all information regarding inaccuracies as well as additional work performed on any of these numbers by posting in the respective table thread. You may also send email to garo at: annie AT teamprimerib DOT com. I have created a thread for discussion on these tables. Note that the latter thread is for discussion on the tables themselves and not on ECM. The old "Report Results here" thread is now closed as results should be reported in the respective table thread.
garo and xilman (aka Paul Leyland)

Last fiddled with by garo on 2005-08-01 at 15:17 Reason: Changed to reflect the new tables with new B1 boundaries.

 2005-01-18, 18:23 #2 garo     Aug 2002 Termonfeckin, IE 22×691 Posts The following is a summary of number of curves that need to be run on a composite before a given level is declared as done. I have taken this snippet from Paul Zimmerman's ECMNet page at http://webloria.loria.fr/~zimmerma/records/ecmnet.html Note that if you used GMP-ECM5.0 the curves must be translated to their ECM6.0 equivalent. Though you really should not be using GMP-ECM5.0 as v6 is much faster!! Code: digits optimal B1 expected curves expected curves (B2=100*B1) (default parameters for ecm-6.0) 20 11,000 84 77 25 50,000 262 206 30 250,000 648 401 35 1,000,000 1,588 948 40 3,000,000 4,716 2,440 45 11,000,000 9,770 4,590 50 43,000,000 18,143 7,771 55 110,000,000 45,841 17,899 60 260,000,000 114,973 43,670 65 850,000,000 193,436 69,351 Finally, numbers marked as resv have been reserved for GNFS/SNFS and thus no further ECM is required on these numbers. Last fiddled with by garo on 2005-08-01 at 15:40
2005-01-20, 10:06   #3
garo

Aug 2002
Termonfeckin, IE

22·691 Posts

I think thiscomment from rogue deserves being repeated here. So starting with 45digits is preferable for composites above 195 bits and at 50 digits is preferable for composites between 146-195 bits.

Quote:
 Originally Posted by rogue 1) that composites < 145 digits are ready for sieving, I assume most of these are reserved 2) that composites > 145 and < 196 should use B1=43e6 (50 bits) at a minimum and have about 1/3 of required number of curves done at that B1 3) that composites > 195 should use B1=11e6 (45 digits) at a minimum

Last fiddled with by garo on 2005-07-28 at 16:02

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