Can someone really help me understand how to get started with this?

[mathgeeks]

Hi i'm a newbie to GIMPS, would really appreicate if someone helps me understand how to get going with things over here?
I also have a bit hard time using PRIME 95, let me be a part of you guys as well.
THANKS AND REGARDS

[mathgeeks]

hey, im so sorry to bring this up out of nowhere but can someone really help me understand how to get started with this? I'm new to GIMPS and have quite a bit issues understanding prime95.
Thanks

[Viliam Furik]

Originally Posted by mathgeeks

hey, im so sorry to bring this up out of nowhere but can someone really help me understand how to get started with this? I'm new to GIMPS and have quite a bit issues understanding prime95.
Thanks

If my name was Kriesel, I would (only) tell you to use the very well-written and pretty much all-topics-covering Reference material. I don't want to wrong Kriesel, so I must say, it is indeed well-written and covers pretty much anything you'd like to know, and even the things you don't know that you don't know. Starting from the top of the link tree (Which may or may not in fact contain some cycles - I didn't look into this, but you can if you want. In case there is some cycle in there, I will urge him to rename it to "Root of the reference graph", instead of the current "Top of reference tree", which is at the bottom of every post in that "tree" - that'd be a LOT of correcting .), if you are told to look somewhere else in the reference material, in the forum, or elsewhere, you are given a direct link to that page, and the link to the top in every post makes it basically fool-proof because you can't get lost in there (unless you don't know about the link at the bottom...). So do use it, it's great!

But I am not Kriesel, so I will also tell you some things directly:

Prime95 can do the following (and more, but pretty much only these things are sensible for a general user):
-- LL and PRP tests of Mersenne numbers, that look for primes. LL, Lucas-Lehmer test, if computed without any error, decides whether it's prime or not. To account for the occasional errors we do another run of the same test called "double-check" to make sure that the result is as correct as it can be under some assumptions of correctness about the program used - there are/were sometimes faulty chips that are/were widespread, e.g. the Pentium bug (I, however, don't know the specifics, as I wasn't aware of GIMPS back then, and possibly not even born yet - quick googling confirms I was not amongst the living yet) which make the computations bad, because in the best case they will be performed absolutely correctly on the software side, but on equally bad hardware, which would produce the exact same results, despite them being incorrect. There were also faulty programs (any Mersenne-oriented program, so the CPU and GPU ones together), a lot more often than hardware, I think. PRP tests are similar, basically identical in time required, but they have few differences other than the obvious difference in name caused by the different tests being used, namely they are PRobable Prime tests, which means (assuming no errors) that if it says the number is not prime, it is not prime for sure, and if it says that it is a prime, it almost certainly the case, but to be sure, LL tests are run to confirm the primality of the Mersenne number; they allow us to easily verify their correctness without running them again by doing few specific computations along the way and making a proof file, that goes on to verification, and if all is good, it guarantees there were no errors during the test, and the result is correct - whatever the result is, it is correct, so not prime is not prime, and a prime result should be verified by LL.
-- P-1 factoring is done to find factors of Mersenne numbers that are relatively easy to find. If a factor is found, the need for a test is gone, because it is obviously not prime.
-- PRP-CF and ECM: PRP-CF is a PRP test done on Mersenne numbers with some factors, that determines whether there are any remaining factors to be found, or whether the last chunk (a cofactor) is a probable prime (same behavior as with normal PRP, but you can't use LL tests for these). ECM is another way of factoring Mersenne numbers.

There is also one big category of work, trial factoring, which should be done on GPUs because CPUs are much better with LL and PRP, and it is basically a waste of time to do TF with them, as GPUs are in most cases more than 100 times faster at it.

That's about it. Feel free to ask about anything.

[kriesel]

The reference info is a collection I've been working on for years. It started as what I would have liked to have found already available for getting started in GPU GIMPS computing, when I joined the forum years ago, and has expanded to book size, and covering GPU, CPU, and cloud GIMPS computing. It has been iterated upon frequently and will be further in the future as things change (proof generation being a recent example), as people ask questions which aren't quite covered yet, errors are identified, etc. Newcomers play a vital role in improving it, providing new eyes to find gaps and errors, and bringing new perspectives and questions

Viliam did a fine job of describing common work types for searching for new Mersenne primes. (But not in time order.)
The sequence for a given exponent is (assuming prime95 or mprime is in use):

• TF first. If no factor found, continue; if factor found, stop effort on this exponent until the factor-hunters follow years later. TF when possible really should be done on GPU with mfaktc or mfakto, not on CPU.
• P-1 factoring next (ideally with enough ram allowance before it's started, to be able to do adequate bounds). If no factor found, continue;
• PRP first test, with software capable of doing proof generation, and sufficient disk space available and allowed, to do a near-optimal proof generation power.
• A fast cert (proof verification) on prime95 / mprime, which usually is successful and almost always concludes showing the exponent composite without finding a factor. ( > 999,999 per million tests). For exponents that had a Lucas-Lehmer first test performed already, PRP/proof double check is a more effective method than LL DC because the speed is equal but the reliability is far higher. Certs are often completed within hours of the PRP first test.
• If for the first time a PRP-P result is obtained (estimated chance ~0.65 per million in 100M to 332M exponent span), keep it secret except for its report to the server, until multiple confirmatory LL tests have completed and an official mersenne.org press release has been prepared and released.

There is also a several year backlog of double checking old LL tests on exponents from ~60M up to ~105M. Running some double checks initially is quicker and a good way to practice running the software, and required for qualifying a system for getting first-test assignments.

A concept to learn about early is the category structure in the assignment rules. Assignment rules for first time PRP are not stated but are more or less the same as for LL that are stated there.

[chalsall]

Originally Posted by kriesel

The reference info is a collection I've been working on for years.

And, if I may please blow some sunshine, is a remarkable body of work.

Few appreciate how important curation at this level of detail is.

Well done sir. Sincerely.

[Mark Rose]

Originally Posted by chalsall

And, if I may please blow some sunshine, is a remarkable body of work.

Few appreciate how important curation at this level of detail is.

Well done sir. Sincerely.

Much of that should probably be added to mersenne.org.

[kriesel]

Originally Posted by Viliam Furik

If my name was Kriesel, I would (only) tell you to use the very well-written and pretty much all-topics-covering Reference material. I don't want to wrong Kriesel, so I must say, it is indeed well-written and covers pretty much anything you'd like to know, and even the things you don't know that you don't know. ... So do use it, it's great!

I give new folks a few answers and tell them where to find the reference info from the beginning, along with a welcome typically. When some persist in acting helpless after that, I think spoon-fed answers reward poor behavior, and stop giving answers. What other users do after that is their call.

Originally Posted by chalsall

And, ... is a remarkable body of work.

Few appreciate how important curation at this level of detail is.

Originally Posted by Mark Rose

Much of that should probably be added to mersenne.org.

I've suggested mersenne.org add some links into it. Hasn't happened.

After initially developing the beginnings of the reference info for my own use, it made no sense to hoard it. It is the better for many eyes on it. I occasionally get a helpful PM pointing out where I got something wrong, omitted something, or content has become outdated.
Documentation is something I can do, so our amazing programmers can do what they do best, perhaps spending less time on user questions and documentation, allowing a little more on code development. Thanks all for the kind words of encouragement, and also for what you do for the project. And note the many people credited with contributing in some way at the bottom of the reference info's monster table of contents page (at Viliam's link above).

[Viliam Furik]

Originally Posted by Mark Rose

Much of that should probably be added to mersenne.org.

I agree. It should also be somehow somewhere linked on mersenneforum, where it would be clearly (as much as it gets) visible for newcomers, and everybody else.

[kriesel]

Originally Posted by Viliam Furik

I agree. It should also be somehow somewhere linked on mersenneforum, where it would be clearly (as much as it gets) visible for newcomers, and everybody else.

All those posts responding to newcomers including links to the reference info serve as breadcrumbs in the forest of threads. And a sticky thread lodged here in the Information and Answers subforum https://mersenneforum.org/forumdisplay.php?f=38 points to it. And a pointer at the end of the old sticky thread too; various posts toward the end of Available software for pursuing mersenne primes sticky thread in GPU computing subforum, the GPU LL testing FAQ sticky thread and elsewhere. Yet people manage to miss them all or just ask without reading or looking first. What more would you suggest?

[mathgeeks]

Originally Posted by kriesel

The reference info is a collection I've been working on for years. It started as what I would have liked to have found already available for getting started in GPU GIMPS computing, when I joined the forum years ago, and has expanded to book size, and covering GPU, CPU, and cloud GIMPS computing. It has been iterated upon frequently and will be further in the future as things change (proof generation being a recent example), as people ask questions which aren't quite covered yet, errors are identified, etc. Newcomers play a vital role in improving it, providing new eyes to find gaps and errors, and bringing new perspectives and questions

Viliam did a fine job of describing common work types for searching for new Mersenne primes. (But not in time order.)
The sequence for a given exponent is (assuming prime95 or mprime is in use):

• TF first. If no factor found, continue; if factor found, stop effort on this exponent until the factor-hunters follow years later. TF when possible really should be done on GPU with mfaktc or mfakto, not on CPU.
• P-1 factoring next (ideally with enough ram allowance before it's started, to be able to do adequate bounds). If no factor found, continue;
• PRP first test, with software capable of doing proof generation, and sufficient disk space available and allowed, to do a near-optimal proof generation power.
• A fast cert (proof verification) on prime95 / mprime, which usually is successful and almost always concludes showing the exponent composite without finding a factor. ( > 999,999 per million tests). For exponents that had a Lucas-Lehmer first test performed already, PRP/proof double check is a more effective method than LL DC because the speed is equal but the reliability is far higher. Certs are often completed within hours of the PRP first test.
• If for the first time a PRP-P result is obtained (estimated chance ~0.65 per million in 100M to 332M exponent span), keep it secret except for its report to the server, until multiple confirmatory LL tests have completed and an official mersenne.org press release has been prepared and released.

There is also a several year backlog of double checking old LL tests on exponents from ~60M up to ~105M. Running some double checks initially is quicker and a good way to practice running the software, and required for qualifying a system for getting first-test assignments.

A concept to learn about early is the category structure in the assignment rules. Assignment rules for first time PRP are not stated but are more or less the same as for LL that are stated there.

Hi, I sincerely want to thank each one of you for helping me out ;
Can you please tell that among the test option given on the Prime95 software which one has the most probability of finding a Mersenne prime? Currently I'm running World Record Sized Numbers To Prime Test.
Also I'm not able to create more than 1 worker

Regards

[Dr Sardonicus]

Originally Posted by mathgeeks

<snip>
Can you please tell that among the test option given on the Prime95 software which one has the most probability of finding a Mersenne prime?
<snip>

The short answer is "No." For a given prime p, M_p either is prime, or is composite. What test you run won't affect that.

There is AFAIK no way to tell in advance which prime exponents p are "more likely" to produce Mersenne primes than others. If anyone involved in the project knew, they'd already be on it.

Given that a total 51 Mersenne primes have been found, with all prime exponents to well over 100 million having been tested at least once, it should be clear that the chances of finding a Mersenne prime are exceedingly small.

If your primary motive in participating in the project is to discover a Mersenne prime, you are almost certainly doomed to disappointment, especially if your computing resources are limited.

There is a great deal of work available in eliminating candidates - trial factoring (TF) and P-1 eliminate candidates by finding small factors.