ECM Work and Parameter Choices

R.D. Silverman · 2006-01-30, 14:42

Hi,

I find it interesting that Bruce just found a factor of 11,256+ that is
"only" 48 digits. What is interesting is that he used B1 = 850 million and
that prior searches all missed it. I would have expected a search at 110M
or (almost certainly) 260M to have found this.

Bruce is certainly doing a terrific job. We all hope that he has
continued success.

I am about 95% done with sieving 2,820+. I will then do 2,815-,
followed by 2,833+. Would someone like to take a heavy wack at the
latter with ECM? There are also only two numbers in the 2- table
left undone with exponent less than 800. 2,787- and 2,799-. (2,793- is
being sieved)

Perhaps people might like to take a heavy wack at these?

patrik · 2006-02-07, 22:02

OK, I will run a few curves on 2,833+. Please tell me when I should stop.

Mystwalker · 2006-02-09, 18:48

Having just installed 2 GB RAM (and blend-tested it for ~4 hours), I'll do some work on M787 at 55 digits. I don't know how much it'll be, since I'm not that often at this machine...

R.D. Silverman · 2006-02-13, 16:48

Quote:

Originally Posted by patrik

OK, I will run a few curves on 2,833+. Please tell me when I should stop.

A "few" curves won't help much.

I should finish 2,815- sometime around Feb 24. I will then start 2,833+.

Mystwalker · 2006-02-13, 17:17

It's hard to say what patrik means by "a few" - a year ago, he had 12 GHz available.

When do you expect the start of 2,787-?

patrik · 2006-02-15, 21:16

No factors found so far:
3000 curves with B1=11e6, B2=11e8
2000 curves with B1=11e6, B2=25577181640 (default GMP-ECM)
1745 curves with B1=44e6, B2=184367799126 (default GMP-ECM)

Another 2000 curves with B1=11e6 and (4500-1745) curves with B1=44e6 have run stage 1 with mprime/Prime95 and are awaiting stage 2 with GMP-ECM. I'll make an effort to have them done by Feb 24.

Mystwalker · 2006-02-15, 23:07

patrik:
It seems like the 45 digit level isn't needed anymore:
http://www.mersenneforum.org/showpos...59&postcount=4

Hence, I don't know whether is it efficient to do stage2 for the B1=11e6 curves. Is there someone who can update the tables to a more proper representation of the current ECM effort?
In other words:
How precise are Bruce's words, and is it possible for George to precisely update the tables accordingly?

I think this is quite an issue, as there are probably several people who waste CPU time on digit levels that are virtually impossible to have a factor.

xilman · 2006-02-16, 08:33

Quote:

Originally Posted by Mystwalker

patrik:
It seems like the 45 digit level isn't needed anymore:
http://www.mersenneforum.org/showpos...59&postcount=4

Hence, I don't know whether is it efficient to do stage2 for the B1=11e6 curves. Is there someone who can update the tables to a more proper representation of the current ECM effort?
In other words:
How precise are Bruce's words, and is it possible for George to precisely update the tables accordingly?

I think this is quite an issue, as there are probably several people who waste CPU time on digit levels that are virtually impossible to have a factor.

Yes and no.

It is possible to find very large factors with very small B1 limits. It is possible to miss very small factors with very large B1 limits. There is a function that minimizes the amount of cpu time required to find factors of specified size to a given probability. This function leads to the well-known tables of B1 versus size of factors.

However, the function has a rather flat minimum and it does not matter too much whether the B1 value chosen in practice is particularly close to the optimal value. It does matter to some extent (or we wouldn't bother!) but even quite wide variations will only slow down the computation by a factor of a few.

Paul

patrik · 2006-02-25, 09:17

I've completed the work I plan to do. And I did 2000 more curves. No factors found. Including the work I reported earlier in this thread:

4000 curves with B1=11e6, B2=11e8
4000 curves with B1=11e6, B2=25577181640 (default GMP-ECM)
6500 curves with B1=44e6, B2=184367799126 (default GMP-ECM)

Mystwalker · 2006-02-28, 18:58

I recently completed 100 curves on M787 with B1=11e7 / B2=26e10. Although this can be interpreted as "few", the count will grow stronger in the next time, as I recently moved and did other time-consuming tasks.

What is the status on M815?

R.D. Silverman · 2006-02-28, 21:24

Quote:

Originally Posted by Mystwalker

I recently completed 100 curves on M787 with B1=11e7 / B2=26e10. Although this can be interpreted as "few", the count will grow stronger in the next time, as I recently moved and did other time-consuming tasks.

What is the status on M815?

The linear algebra will finish in 3 days, if nothing goes wrong.

It would be nice to get some of the base 2 numbers less than 800 bits with ECM.

2,833+ is about 60% sieved.

2006-01-30, 14:42	#1
R.D. Silverman "Bob Silverman" Nov 2003 North of Boston 2³×3×313 Posts	ECM Work and Parameter Choices Hi, I find it interesting that Bruce just found a factor of 11,256+ that is "only" 48 digits. What is interesting is that he used B1 = 850 million and that prior searches all missed it. I would have expected a search at 110M or (almost certainly) 260M to have found this. Bruce is certainly doing a terrific job. We all hope that he has continued success. I am about 95% done with sieving 2,820+. I will then do 2,815-, followed by 2,833+. Would someone like to take a heavy wack at the latter with ECM? There are also only two numbers in the 2- table left undone with exponent less than 800. 2,787- and 2,799-. (2,793- is being sieved) Perhaps people might like to take a heavy wack at these?

2006-02-09, 18:48	#3
Mystwalker Jul 2004 Potsdam, Germany 831₁₀ Posts	Having just installed 2 GB RAM (and blend-tested it for ~4 hours), I'll do some work on M787 at 55 digits. I don't know how much it'll be, since I'm not that often at this machine... Last fiddled with by Mystwalker on 2006-02-09 at 18:49

2006-02-13, 17:17	#5
Mystwalker Jul 2004 Potsdam, Germany 3·277 Posts	It's hard to say what patrik means by "a few" - a year ago, he had 12 GHz available. When do you expect the start of 2,787-? Last fiddled with by Mystwalker on 2006-02-13 at 17:19

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2006-02-07, 22:02	#2
patrik "Patrik Johansson" Aug 2002 Uppsala, Sweden 110101001₂ Posts	OK, I will run a few curves on 2,833+. Please tell me when I should stop.

2006-02-15, 21:16	#6
patrik "Patrik Johansson" Aug 2002 Uppsala, Sweden 5²×17 Posts	No factors found so far: 3000 curves with B1=11e6, B2=11e8 2000 curves with B1=11e6, B2=25577181640 (default GMP-ECM) 1745 curves with B1=44e6, B2=184367799126 (default GMP-ECM) Another 2000 curves with B1=11e6 and (4500-1745) curves with B1=44e6 have run stage 1 with mprime/Prime95 and are awaiting stage 2 with GMP-ECM. I'll make an effort to have them done by Feb 24.

2006-02-15, 23:07	#7
Mystwalker Jul 2004 Potsdam, Germany 3×277 Posts	patrik: It seems like the 45 digit level isn't needed anymore: http://www.mersenneforum.org/showpos...59&postcount=4 Hence, I don't know whether is it efficient to do stage2 for the B1=11e6 curves. Is there someone who can update the tables to a more proper representation of the current ECM effort? In other words: How precise are Bruce's words, and is it possible for George to precisely update the tables accordingly? I think this is quite an issue, as there are probably several people who waste CPU time on digit levels that are virtually impossible to have a factor.

2006-02-25, 09:17	#9
patrik "Patrik Johansson" Aug 2002 Uppsala, Sweden 5²·17 Posts	I've completed the work I plan to do. And I did 2000 more curves. No factors found. Including the work I reported earlier in this thread: 4000 curves with B1=11e6, B2=11e8 4000 curves with B1=11e6, B2=25577181640 (default GMP-ECM) 6500 curves with B1=44e6, B2=184367799126 (default GMP-ECM)

2006-02-28, 18:58	#10
Mystwalker Jul 2004 Potsdam, Germany 3×277 Posts	I recently completed 100 curves on M787 with B1=11e7 / B2=26e10. Although this can be interpreted as "few", the count will grow stronger in the next time, as I recently moved and did other time-consuming tasks. What is the status on M815?