Introduction: ECM work done on Cunningham Project composites

[garo]

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

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)

[garo]

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!!

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.

[garo]

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.

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