20201126, 16:33  #1 
Oct 2020
Terre Haute, IN
2^{2}·13 Posts 
Is it possible to test the results of a 10digit exponent on PrimeNet?
There is a specific 10digit number I would like to test as an exponent to see if might yield a prime number but the current system only seems to allow up to ninedigit exponents. Is there a way to test exponents 10 digits or larger? I have a reason for wanting to test this specific exponent.

20201126, 16:52  #2 
"Curtis"
Feb 2005
Riverside, CA
31×149 Posts 
There's a commandline bit of software floating around the forum, factor5. It'll allow you to trialfactor your candidate.
Check the "operation billion digits" subforum, that's where I found it back in the day. 
20201126, 17:24  #3 
Random Account
Aug 2009
U.S.A.
2^{2}×449 Posts 
Factor5 is in the attached zip file. In the world of software, it is a dinosaur. It runs as a console program. General parameter instructions can be displayed by running the program. Note: there are no commas between parameters, only spaces. Good luck.

20201126, 17:57  #4 
"Viliam FurÃk"
Jul 2018
Martin, Slovakia
3^{2}×37 Posts 
If your exponent is less than 2^32=4294967296 (and prime of course ), you can try to factor it with mfaktc (I believe, according to the thread you started, that you have already installed it  if not, please correct me).
As for testing, mlucas, Ernst Mayer's software should be able to test 10digit exponents, AFAIK. If not, it's pointless either way, at least for now, because there is no fast enough hardware for the task. But my only forsure recommendation is to check the number in mersenne.ca database, it goes up to 9,999,999,967 (which is composite BTW). 
20201127, 02:57  #5 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1001011101111_{2} Posts 
To expand on Viliam's point about the exponent being prime: if the exponent is composite, the corresponding Mersenne number has trivially found factors and so is composite. In that case none of the following is necessary. So assuming the exponent is prime:
If using a cpu for trial factoring, use Ernst Mayer's Mfactor, which is several times faster than Factor5 on the same hardware. But if the candidate exponent will fit (is less than 2^{32}), use mfaktc or mfakto on an appropriate NVIDIA or AMD gpu respectively. Gpu trial factoring is generally many times faster than on cpu. (If the exponent is M31, see the double mersenne web site and note a lot of work has already been done.) If asking about primality testing, note that run times are a few months for upper 9digit exponents on a good Radeon VII running a fast recent version of heavily optimized gpuowl, and multiple years for gigadigit exponents. For cpubased primality testing, you can get a sense of runtime scaling by looking at the prime95 benchmark results for several old and new cpu models, in https://www.mersenneforum.org/showthread.php?t=23900 ("Effect of number of workers" posts). On AVX512 systems it can run up to 64M fft length, exponent ~1.169E9, at ~18 months to complete on a 68 core Knights Landing 7250 as a single worker, or on an i51035g1, about 6 years. Extrapolating upward from 10^{9} would go roughly proportional to p^{2.1}, which gives a factor of ten larger exponent requiring a factor of 126. longer primality test run time. So if 1/10 your candidate exponent takes a month, your candidate takes about 10.5 years. Mlucas can handle somewhat higher exponent (up to 2^{32}), but does not escape the runtime scaling. (Mlucas is likely ready for or being modified for F33.) Some versions of gpuowl can primality test low10digit numbers although the run times are long even on a memoryoverclocked Radeon VII. See also https://www.mersenneforum.org/showpo...4&postcount=12 for some realworld timings on different software, exponents, and hardware over a wide exponent range, 50Mdigit to 1Gigadigit. Between TF and primality testing, there is usually opportunistic P1 factoring. Typically the time taken for optimizing probable time savings, is about 1/40 of the primality test time, or in the 10.5 year example, about 3 months. TF would take weeks or months first. See https://www.mersenneforum.org/showpo...23&postcount=6 for why. Mersenne.ca does reservations for TF for p>1G, as does the double mersenne site. To my knowledge there's no reservation system for P1 factoring or primality testing for p>1G. Last fiddled with by kriesel on 20201127 at 03:47 
20201127, 03:49  #6 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
37×131 Posts 

20201127, 05:39  #7  
Oct 2020
Terre Haute, IN
2^{2}·13 Posts 
Quote:
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20201127, 05:44  #8 
Oct 2020
Terre Haute, IN
64_{8} Posts 
Just an observation about primes that I made about 35 years ago, when I was in high school, that makes me wonder about the exponent in question. I'll elaborate if I find something. :)

20201127, 07:19  #9 
"Curtis"
Feb 2005
Riverside, CA
31·149 Posts 

20201127, 07:33  #10  
Oct 2020
Terre Haute, IN
2^{2}×13 Posts 
Quote:
I'm on my office computer at the moment and our firewall won't let me access that link because it's a foreign IP address, but I'll have to check it out later. 

20201127, 14:02  #11  
Oct 2020
Terre Haute, IN
34_{16} Posts 
Quote:
Quote:


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