[quote=cheesehead;230539]I think I was having low blood sugar when I wrote that one. That tends to narrow ones thinking. Sorry, I didn't recognize that at the time.[/quote]
cheesehead,

No problem. And I understand: I keep my own tank topped up when I'm working.

Rodrigo

This thread has good questions and good answers.

I just want to add that I too would appreciate a little fine-tuning and standardization of the nomenclature.

[I]Possibly completely new options could be added, but that's part of my wish to make this project as optimized and coordinated a factoring project as it is a prime finding project. So that should be the topic for another thread.[/I]

lorgix,

The funny thing is that, soon after this thread, the disparate labels somehow started making sense to me. Maybe it's because writing for the thread made me think about them harder than before. Or maybe I simply got reeled into the Matrix...

I'd be curious to hear your ideas about adding "completely new options." Start a new thread with a title like that, and let's see what happens.

Rodrigo

I'm assuming the goal is to keep the interface and terminology as simple as possible without losing functionality. So calling what is essentially the same thing different names in different places isn't in our interest.


Regarding factoring;

I'm talking about factoring that is beyond that which is currently assigned through GIMPS.
[URL]http://www.mersenneforum.org/showthread.php?t=13302[/URL]
The above link leads to a thread regarding factoring numbers with exponents smaller than 5000000; clearly not directly connected to the [B]G[/B]reat [B]I[/B]nternet [B]M[/B]ersenne [I][B]P[/B]rime[/I] [B]S[/B]earch.

Some other people have asked pretty much the same questions as me, but I can't seem to find the threads...

I've been planning to try and straighten this out a bit before starting a thread about it, if a new one is necessary that is. There may already be one out there.

Certainly there are a lot of "sub-projects" going on... and a lot of esoteric terminology and jargon can make it harder to find the right place.

[U]I'm gonna try to crystallize the essence of the concept here;[/U]

GIMPS and PrimeNet are optimized for finding new and, in most cases, bigger primes. Or at least that's the goal.

This is done by coordinated, distributed work. Making reservations, keeping track of progress etc. And calculating the optimal amount of TF and P-1 to do, in order to save LL tests.

I would like Prime95 and PrimeNet to also have a "factoring option" or something to that effect. Having the goals of
1. Fully factoring Mersennes.
2. Finding factors to known composite Mersennes.
3. Finding factors to any Mersenne.

[B]PrimeNet&GIMPS:Prime finding::[what I'm thinking of]:Factor finding[/B]

A lot of work that falls into this category is being done, and some is also more or less coordinated through this forum. I'd like to see it implemented in the system.

The extent to which different algorithms are applied would then be determined with the goal of finding factors.

There is ofc overlap between this and how the system operates today. But once a number is declared composite (by testing or factoring) the following efforts to factor it can often times be described as a scrambled mess.

I can think of several ways to go about this... One could assign the task that is most likely to yield a new factor, given the hardware and time at hand. One could aim to maximize efficiency by working on what should give the highest [factor size squared]/[effort], (roughly... you get the point, hopefully). One could also allow users to choose to concentrate their efforts to a range or a single number, optimizing parameters given conditions like hardware etc. We might also be able to combine P-1 and ECM efforts better. And avoid the same P-1 being done several times.

[B]How this relates to your question about new options:[/B]
Various options aiming for the smallest not yet completely factored number, the smallest number without known factors, work mode (P-1, ECM, TF..), work unit size.... and/or combinations of a number of those.

I'm sure you get the idea.

[B]Anyone reading this:[/B]
1. Please make some noise if you think this idea is good.
2. Please explain any flaw you see.
3. Please point out any thread already dealing with this or related matters.

Wow... big post.. think I'm starting to ramble. Anyway, just putting it out there. If there is some interest; there will be a new thread. Hopefully less rambling.

Let's Put This in Its Own Thread
 

To the Forum Gods:

This is very interesting and, for maximum exposure, IMHO deserves to be in its own thread!

Rodrigo

lorgix,

I'm asking the Forum administrator to put this in its own thread, as it really deserves to stand out and be seen.

I'm relatively new here, and not a mathematician, so I'm far from the most qualified person to comment on your proposals. But they certainly deserve a hearing, and I'm not aware of the issues being discussed extensively before. But if they have been, then at the very least this might serve to reprise the topic.

My first thought would be that the goal of GIMPS really is to find new Mersenne primes, and so once a number has been shown not to be prime there is no purpose in trying to factor it completely; but I could be wrong and I sure would like to hear what more knowledgeable members have to say about this.

And yes, there are a number of independent or semi-independent projects covered in this forum, which can contribute to the "chaotic" impression. I myself am contributing one of my PCs to Operation Billion Digits, which is one of the ones I understand better. That said, I'm not sure if these other projects could or should be more formally incorporated into GIMPS and/or the Prime95 software (the latter would imply more work for the project's founder :wink:), but again this is an interesting topic and I'd be curious to see what other people have to say.

Thanks for bringing up these issues.

Rodrigo

I too think the idea deserves a thread, I'm just not certain it doesn't already exist.

You are correct, trying to completely factor a number isn't directly related to finding new primes. I should add that I don't hold any math degree either.

But factoring numbers can help further our understanding of numbers.

I guess we should also consider the fact that this computing is already being done.

That leaves us with two conditions to be met:

1. Sufficient interest from project participants.
2. Interest from the people behind the project.

Those things said, factoring is essential to the [B]G[/B]reat [B]I[/B]nternet [B]M[/B]ersenne [B]P[/B]rime [B]S[/B]earch as it is. Could we possibly make that factoring more efficient, while at the same time making the above mentioned (sub-projects and such) more efficient and coordinated?

Frankly, I don't think the two concepts are competing (and why would they?). People who really want to split M1061 will be working on that, and people who dream about finding the first 10^[some integer larger than 7]-digit prime will be looking for that.
The question is (in other words this time); is there enough interest to incorporate these ideas/develop the project in this direction to some extent?

A lot of stuff going on in this forum is beyond my knowledge. But if I get =>1 informed and though through response(s) to this, then =>1 person(s) will learn something from this. :smile:

[QUOTE=Rodrigo;235458]My first thought would be that the goal of GIMPS really is to find new Mersenne primes, and so once a number has been shown not to be prime there is no purpose in trying to factor it completely;[/QUOTE]

There is no purpose in trying to find new Mersenne primes. They're not useful for anything. We do it because it interests and entertains us. Some of us are also interested and entertained by finding factors of known-composite Mersennes, even if that doesn't contribute to the effort to find primes.

The official goal of GIMPS is indeed to find new Mersenne primes. But I think we can infer other goals from what GIMPS actually does. Specifically it is a [I]de facto[/I] goal to learn as much as we can about the factors of prime-exponent Mersenne numbers. Every such number can be placed in one of four ranks, based upon what we know about its factors:

1. We know nothing about its factorisation.
2. We know that it is composite, but we don't know any factors.
3. We know at least one factor.
4. We know its complete factorisation.

Note that known Mersenne primes are rank 4. If we know a number is prime, we know its complete factorisation.

Viewed through the lens of this secondary goal, there are some deficiencies in the exponent status report in the case where at least one factor is known. First, it no longer reports factoring limits, which it would be useful to know if we are to do further factorisation work on the number. Secondly it does not keep track of whether the cofactor has been tested for primality, and if so, what was the result. Consequently, we may know a Mersenne number's complete factorisation (because its cofactor is actually prime), but not know that we know it (because the cofactor has not been tested, or the results of a test have not been recorded).

[QUOTE=Mr. P-1;238172]
Viewed through the lens of this secondary goal, there are some deficiencies in the exponent status report in the case where at least one factor is known. First, it no longer reports factoring limits, which it would be useful to know if we are to do further factorisation work on the number. Secondly it does not keep track of whether the cofactor has been tested for primality, and if so, what was the result. Consequently, we may know a Mersenne number's complete factorisation (because its cofactor is actually prime), but not know that we know it (because the cofactor has not been tested, or the results of a test have not been recorded).[/QUOTE]

Yes! I've been thinking about this for a while. We don't know what work has been done on numbers with known factors, except ECM.

[QUOTE=lorgix;238225]Yes! I've been thinking about this for a while. We don't know what work has been done on numbers with known factors, except ECM.[/QUOTE]


Yes. The ECM status page by default shows exponents up to 2500. Since all of them have been ECMed to the 40 digit level, there's really no point in doing further TF, regardless of how much TF has actually been done. It's also a safe bet that the cofactors are known composite, and that they've been adequately P-1ed. However as you go further up the chart, these assumptions become more and more dubious.

[QUOTE=Mr. P-1;238230]Yes. The ECM status page by default shows exponents up to 2500. Since all of them have been ECMed to the 40 digit level, there's really no point in doing further TF, regardless of how much TF has actually been done. It's also a safe bet that the cofactors are known composite, and that they've been adequately P-1ed. However as you go further up the chart, these assumptions become more and more dubious.[/QUOTE]

Doing P-1 on larger numbers with known factors could be of interest. But again, with all previous efforts being obscured as soon as a factor is found...

I'm guessing database size is a problem.