Is it possible to test the results of a 10-digit exponent on PrimeNet?

[piforbreakfast]

There is a specific 10-digit 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 nine-digit exponents. Is there a way to test exponents 10 digits or larger? I have a reason for wanting to test this specific exponent.

[VBCurtis]

There's a command-line bit of software floating around the forum, factor5. It'll allow you to trial-factor your candidate.
Check the "operation billion digits" subforum, that's where I found it back in the day.

[storm5510]

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.

[Viliam Furik]

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 10-digit 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 for-sure recommendation is to check the number in mersenne.ca database, it goes up to 9,999,999,967 (which is composite BTW).

[kriesel]

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 2³²), 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 9-digit exponents on a good Radeon VII running a fast recent version of heavily optimized gpuowl, and multiple years for gigadigit exponents.

For cpu-based primality testing, you can get a sense of run-time 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 i5-1035g1, about 6 years. Extrapolating upward from 10⁹ 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 2³²), but does not escape the run-time scaling. (Mlucas is likely ready for or being modified for F33.) Some versions of gpuowl can primality test low-10-digit numbers although the run times are long even on a memory-overclocked Radeon VII.
See also https://www.mersenneforum.org/showpo...4&postcount=12 for some real-world timings on different software, exponents, and hardware over a wide exponent range, 50Mdigit to 1Gigadigit.

Between TF and primality testing, there is usually opportunistic P-1 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 P-1 factoring or primality testing for p>1G.

[kriesel]

Originally Posted by piforbreakfast

I have a reason for wanting to test this specific exponent.

What's the exponent? What's the reason? (Hopefully not "My social security number or bank account number is prime so I wondered about the corresponding Mersenne number")

[piforbreakfast]

Originally Posted by storm5510

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.

I downloaded the zip file and unpacked the program but absolutely nothing is happening when I try to run it. Is there something else I need to do?

Originally Posted by Viliam Furik

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 10-digit 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 for-sure recommendation is to check the number in mersenne.ca database, it goes up to 9,999,999,967 (which is composite BTW).

The exponent in question is prime. I don't have mfaktc or mlucas installed but would very much like to know where to find those programs.

[piforbreakfast]

Originally Posted by kriesel

What's the exponent? What's the reason? (Hopefully not "My social security number or bank account number is prime so I wondered about the corresponding Mersenne number")

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. :)

[VBCurtis]

Originally Posted by piforbreakfast

I downloaded the zip file and unpacked the program but absolutely nothing is happening when I try to run it. Is there something else I need to do?

Is it giving you an error? You're running it from the command line, right?

[piforbreakfast]

Originally Posted by kriesel

(If the exponent is M31, see the double mersenne web site and note a lot of work has already been done.)

Well dangit, I didn't notice this tidbit until just now. M31 was in fact the exponent I was wanting to test. I guess brilliant minds think alike.

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.

[piforbreakfast]

Originally Posted by kriesel

(If the exponent is M31, see the double mersenne web site and note a lot of work has already been done.)

Originally Posted by piforbreakfast

Well dangit, I didn't notice this tidbit until just now. M31 was in fact the exponent I was wanting to test. I guess brilliant minds think alike.

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.

I hope I'm not coming across as pompous for being the new kid on the block and suddenly thinking I have a blockbuster idea that nobody here has thought of before. Since losing my wife in June I've had way too much time on my hands and have dug up long-dormant intellectual pursuits that I hadn't had time for in years or decades. This site and this project just happens to be one spot where I've landed, and I hope I can find the intellectual stimulation here that I'm looking for.