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Old 2016-12-14, 22:20   #12
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Originally Posted by petrw1 View Post
I listed the latest B1/B2 on record and who did that test.
If any any you still have the the save files PM me.
I already started working in these ranges recently. We should definitely co-ordinate to avoid duplication of effort.

I have 7127, 7621 and 8291 with B1=100,000,000,000, and most of the others to B1=10,000,000,000 or better (the range above M17,000 still has a few more days to complete). I haven't manually reported them yet because I will do stage 2 later.

For these small exponent ranges Stage 2 is best done with GMP-ECM, and I have already done some. For instance I already did 10399 and others with B1=10,000,000,000 and B2=505,851,529,607,770 , with no factors found. This was done in the cloud with a bit more than 32 GB of memory. Unfortunately, negative gmp-ecm results can't be reported to PrimeNet, I think it's necessary to e-mail George or something.

Even though I'm working on these myself, I'm somewhat pessimistic. I think Bob Silverman was of the opinion that it was more useful to throw more ECM at them instead of taking P−1 to very high levels. Recall that some factors are basically invisible to P−1 (the ones that happen to have non-smooth k). I'm finding a bunch of second, third and higher factors, but any exponents that still have no known factors have already been tested with ECM to a pretty large depth without success.

I'm not sure if 16GB is enough. I'm generally using between 32 and 64 GB using cloud instances.

I am looking forward to availability of the recently announced AWS Batch, which will allow doing batch jobs in the cloud. You can just specify the number of cores and the amount of memory, and the job will get scheduled for you without you having to manage the virtual machine instances yourself.
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Old 2016-12-15, 03:31   #13
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I already started working in these ranges recently.

Even though I'm working on these myself, I'm somewhat pessimistic. I think Bob Silverman was of the opinion that it was more useful to throw more ECM at them instead of taking P−1 to very high levels.

I'm not sure if 16GB is enough.
OK then I will stick to plan A. I have 15 or 20 cores ready to ECM all un-factored exponents under 20,000; 100 curves at a time.

P.S. Does GMP-ECM make a BIG difference for Stage 2 for exponents of this size?
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Old 2016-12-15, 05:19   #14
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Can you KEEP the stage 1 files? Is there a server available where we can collect them? Much easier to extend later, avoiding lots of duplicate effort. I have many of those from past efforts, but looking to the numbers in your table, I am far behind, and they can not really be used.
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Old 2016-12-15, 07:34   #15
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If anyone would like the save files for the 25 numbers that I worked on which pertw1 listed, I can PM you. It will not save you much though, maybe 35 GHzD in all.
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Old 2016-12-15, 09:23   #16
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Can you KEEP the stage 1 files? Is there a server available where we can collect them? Much easier to extend later, avoiding lots of duplicate effort.
Yes, I am retaining all of these files, they are stored in the cloud. By default, mprime does not delete them. They aren't very big at all, for instance m0019997 is only 2640 bytes.

Note however that if you have the standard NumBackupFiles=3 in your prime.txt, then mprime will also retain the .bu and .bu2 files (frankly this seems like a bug), and these can be huge, presumably because they reflect the high memory usage during stage 2. To avoid this, I always set NumBackupFiles=1 in any working directory where I'm doing P−1 testing.

At the moment they aren't setup for public retrieval, but it would be possible to do so by creating a static website via Amazon S3 for that purpose.
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Old 2016-12-15, 11:00   #17
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P.S. Does GMP-ECM make a BIG difference for Stage 2 for exponents of this size?
Yes, it makes a very big difference for small exponents, especially for the very smallest. It does stage 2 in O(sqrt(n)) time rather than O(n), but at the cost of using a lot more memory.

For example, James Hintz this past September did a P−1 test of M1619 (no known factors) using B1=3,790,662,020,300 and B2=303,252,961,624,000 (about 3.0 × 1014). Using GMP-ECM for stage 2 instead of mprime, you could easily surpass this B2 value in fairly short order. And if you threw a really large amount of memory at it, say up to 64 GB, you could even take it to B2 = 1017 in a few hours.

It might be worth contacting him if anyone knows how, to see if he still has the savefiles. Nevertheless, the odds of finding a factor with P−1 are extremely small, given the amount of ECM testing that has already been done (to the t=60 level).

The same principle would apply with ECM testing, it's best to use GMP-ECM for stage 2.
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Old 2016-12-15, 22:18   #18
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Originally Posted by GP2 View Post

The same principle would apply with ECM testing, it's best to use GMP-ECM for stage 2.
I´ve done some experiments in the past to compare using Prime95 only vs Prime95 for Stage 1 and GMP-ECM for Stage 2, and for exponents up to 10K it definitely pays to use the combo. The smaller the exponent the larger the gain: for M1277, the combo P95+GMP-ECM would theoretically find a factor in - 1/5 of the time taken by P95 only.
I´m still running ECM curves on small exponents, and I will continue doing it throughout next year. I have already managed to find a first factor for a 15K and another for a 20 K exponent, and several others fo exponents under 100K, and my goal for next year is to find a first factor for a sub-10K exponent. It´s probably too ambitious, as I have only an i5-750 with 16GB of DDR3-1600 memory dedicated to the job, but hey, I´m with GIMPS for nearly 15 years, have done lots of DC, P-1 and some 1st time LL in the past, not to mention large amounts of TF on GPUs, and now it´s time to do something different.
After all, the most important thing is to have fun, isn´t it?
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Old 2016-12-15, 22:44   #19
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Quote:
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Yes, it makes a very big difference for small exponents, especially for the very smallest. It does stage 2 in O(sqrt(n)) time rather than O(n), but at the cost of using a lot more memory.
How much is "... a lot more memory ..." I have as little as 4G on some of the PC's I want to run this on.
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Old 2016-12-15, 22:56   #20
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Quote:
Originally Posted by petrw1 View Post
How much is "... a lot more memory ..." I have as little as 4G on some of the PC's I want to run this on.
You can always use the -maxmem switch to limit how much it uses.

I'm testing 4007 and with B1=2.9B I need to use -maxmem=14000 to avoid it crashing when it tries to use more than 16gig
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Old 2016-12-16, 02:12   #21
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You can always use the -maxmem switch to limit how much it uses.
Yes, but in doing so you lose some of the benefit of using gmp-ecm

Let's say you want to do an exponent to B2 = 100,000 but you only have enough memory to do B2 = 1000 (I'm using ridiculously low values in order to simplify the example).

No problem, you say, I'll just run gmp-ecm 100 times, specifying a different range for B2 each time:

    0-1000
 1000-2000
 2000-3000
...
99000-100000

and that will take 100 times as long as doing only B2 = 1000.

However, because GMP-ECM uses an O(sqrt(N)) algorithm for stage 2, if you had enough memory to do B2 = 100,000 in one shot instead of in a hundred separate runs, then that would only take 10 times as long as doing B2 = 1000.

So in that scenario, the low-memory machine either takes ten times longer than the higher-memory machine, or has to use a B2 limit that is ten times smaller than the higher-memory machine.

Last fiddled with by GP2 on 2016-12-16 at 02:28
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Old 2016-12-16, 02:24   #22
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Originally Posted by petrw1 View Post
How much is "... a lot more memory ..." I have as little as 4G on some of the PC's I want to run this on.
"The more, the better"

From memory and off the top of my head, if you are running GMP-ECM and you increase B2 by 10 times and leave everything else the same increases both the memory and the run time by about 2.5 to 3 times.
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