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-   -   ECM Work and Parameter Choices (https://www.mersenneforum.org/showthread.php?t=5410)

R.D. Silverman 2006-01-30 14:42

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. :bow:

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=patrik]OK, I will run a few curves on 2,833+. Please tell me when I should stop.[/QUOTE]


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, [url=http://www.mersenneforum.org/showpost.php?p=50105&postcount=50]he had 12 GHz[/url] 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:
[url]http://www.mersenneforum.org/showpost.php?p=71059&postcount=4[/url]

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. :sad:

xilman 2006-02-16 08:33

[QUOTE=Mystwalker]patrik:
It seems like the 45 digit level isn't needed anymore:
[url]http://www.mersenneforum.org/showpost.php?p=71059&postcount=4[/url]

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. :sad:[/QUOTE]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=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?[/QUOTE]

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.


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