20210120, 17:50  #1 
Feb 2019
2^{2}×7 Posts 
What is the most efficient way to run math programs (large numbers)?
Hi there,
If I want to calculate with large numbers and I am looking for the option where the arithmetic operations can be carried out the fastest, what is the best way to proceed? The situation for me is like this: I have an old computer (Intel Core 2 Duo). Should I buy a new computer with a large RAM and a graphic board where I can run the math programs or should I use azure or aws with a possible GPU workstation or should I contact a university and ask them whether I can use their mainframe and book time slots or cores or both? If I use cloud computing, I would be willing to invest 50 euros (60 USD) a month, it could also be that I book many cores so that it can be calculated faster and the 50 euros are used up after a few days. That would be ok too, my limit would simply be 50 euros per month. For a new computer, I could currently invest between 500800 euros (6001000 USD). What is the best way to proceed? Does anyone have a tip for me? 
20210120, 18:06  #2 
Sep 2002
Database er0rr
3673_{10} Posts 
"Calculate large numbers" could mean several things. What do you mean? In what time scale? If it is to do with large primes then you have several options in ascending magnitude: Pari/GP, Perl or GMP or GWNUM based softwares, even possibly Mlucas. If it was Mersenne Numbers and you have a GPU then gpuOwl might be an option.
As for which hardware to use, I'd recommend a many core AMD box over cloud computing. Cloud computing can be had for free if you are prepared to be patient and learn to use and nurse it. Last fiddled with by paulunderwood on 20210120 at 18:20 
20210120, 18:59  #3 
"Curtis"
Feb 2005
Riverside, CA
3^{4}×59 Posts 
Figure out what software does the calculations you want, then see how fast that software is on a desktop you can afford, or a free core like Google Colab, or a paid core like AWS.
Without knowing what software you want to run, we can't give a useful answer for what hardware is best for you. You were really vague about the math side, so there really isn't much to go on. 
20210121, 12:09  #4 
Feb 2019
2^{2}×7 Posts 
I see, it makes sense to describe what I mean exactly, when I write that I want to calculate with large numbers. I will gladly explain this in more detail.
I am interested in the following mathematical topics: Search for Mersenne primes with 2 ^ p  1> 2 ^ 82589933 1 verification of the strong Goldbach conjencture for n> 4 x 10 ^ 18 verification of odd perfect numbers for n> 10 ^ 1500 Which software and which hardware should I use in the mentioned cases? So far I only know which software I should most likely use to search for the Mersenne prime numbers. 
20210121, 12:30  #5  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
29BA_{16} Posts 
Quote:
If you are particularly interested I could recommend writing your own software, using publicly available sources and algorithms as a starting point. It might take you longer to get faster than the readily available stuff but, to compensate, you will learn a hell of a lot about the subject. 

20210121, 13:37  #6  
"Marv"
May 2009
near the TannhΓ€user Gate
27F_{16} Posts 
Quote:
If you go to the web site mersenne.org, near the top it gives the latest search progress. Today it says "All exponents below 101β066β557 have been tested at least once." Also, if you look at "Current Progress > Recent Results and Recent Cleared", you can see that most of the Mersenne testing is being done on exponents between the one mentioned above and about 106,xxx,xxx. Studying that website may answer your questions about Mersenne searching. 

20210121, 15:33  #7  
"Curtis"
Feb 2005
Riverside, CA
3^{4}·59 Posts 
Quote:
OP Searching for Mersennes can be done quickly on some GPUs. Have a look at the GPUowl threads for an idea of how fast certain video cards are. If you prefer using a CPU for such searching (reasonable, when your other searches aren't likely to make full use of a GPU), be aware that more cores isn't always better for Mersenne searching Prime95/mprime is often memory bandwidth limited, especially on machines with just two memory channels. Lucky for you, there's a ton of benchmark data out there so you can avoid spending extra cash on a cpu that's not really faster for Mersenne hunting. It's going to be hard to verify odd perfect numbers, since we don't know of any. If you mean you would like to contribute to raising the 'xxx' bound of "no odd perfect numbers below xxx", that's done by factoring numbers which is not GPUenhanced at this time. Factorization jobs benefit from tons of cores, but are easily parallelizable for the longest phase of the job (sieving); so, two regular machines is often as good as one fancy machine. 

20210121, 20:01  #8  
Feb 2019
2^{2}×7 Posts 
Quote:
This is exactly what I meant by that, of course I know that there are no known odd perfect numbers, so you can't check odd perfect numbers either. I just expressed myself wrongly, sorry, English is not my mother tongue, sometimes I don't express myself correctly. 

20210122, 11:50  #9  
Feb 2019
34_{8} Posts 
Quote:
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20210122, 15:21  #10 
Dec 2020
Montreal
10_{16} Posts 
From my understanding, this is referring to how GNFS/SNFS sieving jobs can be spread out over multiple instances running on different computers. EdH has a great guide about how to set up a distributed NFS job. https://www.mersenneforum.org/showthread.php?t=23165

20210122, 15:54  #11  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:


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