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Old 2020-04-16, 07:36   #1
jas
 
"Simon Josefsson"
Jan 2020
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Default Best use of high-memory machines?

Hi. I have a couple of machines with larger amounts of memory that I would like to use for the best purpose for GIMPS (with a slight personal bias towards actually making history and find a new prime). The machines have dual Xeon E5 CPUs with 8-12 cores each, such as 2x2673v3, 2x2640v2, 2x2670v1 and have 128GB or 256GB now but could be rearranged into fewer machines but with 512GB or even 1TB of RAM.



I'm doing PRP's now but that doesn't really utilize a lot of the memory. What are the other options?



It looks like P-1 factoring can make use of the memory, but I don't know how to benchmark this in a good way, can someone help? Is there a way to benchmark various parameters such as:


1) Number of CPU cores 1-24
3) Number of workers
2) Amount of memory 32GB, 64GB, 96GB, 128GB, 196GB, 256GB


Currently I am doing some P-1 factoring on my machines, but they are doing PRP's at the same time so it is hard to tell if the P-1 worker is working optimally.


Thanks,
Simon
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Old 2020-04-16, 13:47   #2
kriesel
 
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P-1 is the most memory-hungry of the TF, P-1, primality test sequence of working toward finding the next Mersenne prime by elimination. Up to at least 32GB per P-1 worker is useful. There are many exponents that have not had P-1 factoring applied, or only to very low limits. It's best to go for the full limits initially, not to low limits first as some users do. I suspect applying an entire Xeon to one P-1 worker would be best cache usage and performance. Test for yourself. For the B1 and B2 bounds, I recommend using the PrimeNet values on James Heinrich's site for the exponent;
https://www.mersenne.ca/exponent/332233123 for example.

The approach of testing to full limits immediately, without any other smaller-bounds runs, is what RDS has supported.
See https://www.mersenneforum.org/showpo...9&postcount=20 for test cases performed in gpuowl. These empirically confirmed the RDS position.

Also possibly useful or interesting background are https://www.mersenneforum.org/showpo...7&postcount=12
https://www.mersenneforum.org/showpo...4&postcount=17
https://www.mersenneforum.org/showpo...9&postcount=30

The best way to benchmark P-1 on your hardware is to make actual runs. The probability of finding a factor can be calculated using https://www.mersenne.ca/prob.php
I don't know whether homogeneous (all P-1 on a system) or heterogeneous (mixing P-1 and primality testing on one system) is better performance. With differing computation types there's need for a common basis of comparison. I usually use P-1 runtime vs. P-1factor odds x 2.04 LL tests or x 2 PRP tests.
Please post your benchmark results.

Last fiddled with by kriesel on 2020-04-16 at 14:00
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Old 2020-04-16, 17:07   #3
Prime95
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Sorry to disappoint you, but quantity of RAM is not an important ingredient in finding new Mersenne primes.

Yes, P-1 can use more RAM but it is only slightly beneficial.
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Old 2020-04-16, 17:54   #4
PhilF
 
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If finding huge (really huge) factors sounds interesting, you can put all that memory to use using GNFS or SNFS to find factors for the Cunningham Project.
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Old 2020-04-16, 18:13   #5
kriesel
 
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Quote:
Originally Posted by Prime95 View Post
Sorry to disappoint you, but quantity of RAM is not an important ingredient in finding new Mersenne primes.

Yes, P-1 can use more RAM but it is only slightly beneficial.
Having all memory channels populated improves benchmarks and performance, yes? With an existing system that's already populated with DIMMs of set size, that may mean having a lot more GB installed than is strictly necessary for the data size. For example, I don't need 16GB to run one worker, but it performs much better with two 8GB DIMMs than one on an i7-4790.

Last fiddled with by kriesel on 2020-04-16 at 18:17
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Old 2020-04-16, 19:40   #6
R.D. Silverman
 
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Quote:
Originally Posted by PhilF View Post
If finding huge (really huge) factors sounds interesting, you can put all that memory to use using GNFS or SNFS to find factors for the Cunningham Project.
Indeed. The best use of large memory machines would be to help Greg (frmky) with the
linear algebra. There is a big backlog. Lots of memory does not really help GIMPS.
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Old 2020-04-18, 12:46   #7
xilman
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Quote:
Originally Posted by R.D. Silverman View Post
Indeed. The best use of large memory machines would be to help Greg (frmky) with the linear algebra. There is a big backlog. Lots of memory does not really help GIMPS.
Seconded.
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