Choices for Manual Assignments

[Rodrigo]

Hello,

The choices for manual assignments on this page http://www.mersenne.org/manual_assignment/ are a little different from what we see in the Prime95 "Worker Windows" menu. So I have a couple of questions --

1) What criteria would one use to select "World record tests" vs. "Smallest available first-time tests" (or vice versa)?

2) How or where does "ECM factoring" fit in the GIMPS scheme of things?

Sorry for asking yet more noob questions!

Rodrigo

[mdettweiler]

Originally Posted by Rodrigo

1) What criteria would one use to select "World record tests" vs. "Smallest available first-time tests" (or vice versa)?

The only difference between "World record tests" and "Smallest available first-time tests" is that WRT is constrained to hand out an exponent greater than that of the largest known Mersenne prime. That is, it's guaranteed to be a world record if if it turns up prime; a regular first-pass exponent, by contrast, could be below the world record, still working on filling in lower exponents that have not yet been tested.

Currently, the lowest exponent without an LL test is in the vicinity of 36M; however the largest known Mersenne prime is M43112609. See http://www.mersenne.org/primenet/ for a detailed breakdown; any of the numbers in the "LLERR" and "NO-LL" columns between 36M and 43M are fair game for "Smallest available first-time tests" but not "World record tests".

Note that many of the exponents in those "holes" below 43112609 are currently assigned, so the lowest available unassigned number at any given moment may be greater than the world record, in which case the two options will be identical. The main difference is that WRT is guaranteed to give you something bigger than the world record.

2) How or where does "ECM factoring" fit in the GIMPS scheme of things?

ECM (Elliptic Curve Method) is a factorization method which is somewhat more resource-intensive than trial factoring, but can find much bigger factors. Each individual ECM curve is run on a random starting value (called the sigma); it's a probabilistic method, so as you complete more curves at a given bound, the probability of your having found a factor of a given size increases. Thus, the Primenet server hands out individual curves to clients for a given number until a certain factor size level has been cleared; then it moves on to a higher bound for the next factor size level.

ECM is actually very similar to P-1 (IIRC, it's a generalization of that method). However, due to its relative resource-intensiveness, it is not a practical method of removing factors from potential prime candidates. Rather, it's used on much lower, known-composite numbers to further efforts to get their complete factorizations.

Note that even though ECM and P-1 are related, P-1 is NOT a probabilistic method. If there is a factor that will be found by P-1 at a given bound, then one run of P-1 will find it. ECM, however, is never guaranteed to find a factor after a given number of curves.

[Rodrigo]

mdettweiler,

Thanks very much for the excellent, detailed explanation!

You lead me to a follow-up question:

How are the "World record tests" and "Smallest available first-time tests" on the manual assignments page, different from the "First time tests" in the Worker Windows?

I guess that, at bottom, what I'm wondering about is the reason for the difference in the nomenclature -- why don't the manual assignments page and the Prime95 menu simply offer the same choices with the same names? They offer some of the same work options, but then also different ones. Is there a reason for the differing but overlapping sets of options?

Rodrigo

[mdettweiler]

Originally Posted by Rodrigo

mdettweiler,

Thanks very much for the excellent, detailed explanation!

You lead me to a follow-up question:

How are the "World record tests" and "Smallest available first-time tests" on the manual assignments page, different from the "First time tests" in the Worker Windows?

I guess that, at bottom, what I'm wondering about is the reason for the difference in the nomenclature -- why don't the manual assignments page and the Prime95 menu simply offer the same choices with the same names? They offer some of the same work options, but then also different ones. Is there a reason for the differing but overlapping sets of options?

Rodrigo

They both offer the same work options, just worded differently. For instance, "Smallest available first-time tests" on the website = "First time tests" in Worker Windows. Similarly, "World record tests" = "World record sized numbers to test"; "TF-LMH" = "Trial factoring to low limits"; etc.

[Rodrigo]

Originally Posted by mdettweiler

They both offer the same work options, just worded differently. For instance, "Smallest available first-time tests" on the website = "First time tests" in Worker Windows. Similarly, "World record tests" = "World record sized numbers to test"; "TF-LMH" = "Trial factoring to low limits"; etc.

Thanks, mdettweiler, this is a great help!

Knowing the situation as you do -- Could I put in for a change to standardize the nomenclature from one to the other (website to software)? For example, except for your patient explanation I wouldn't have known that "first-time tests" are the same as "smallest available first-time tests," or that "trial factoring to low limits" is the same as "TF-LMH." Surely there are other folks out there scratching their heads, but too embarrassed to ask?

Rodrigo

[cheesehead]

Originally Posted by Rodrigo

1) What criteria would one use to select "World record tests" vs. "Smallest available first-time tests" (or vice versa)?

Originally Posted by mdettweiler

The only difference between "World record tests" and "Smallest available first-time tests" is that WRT is constrained to hand out an exponent greater than that of the largest known Mersenne prime. That is, it's guaranteed to be a world record if if it turns up prime; a regular first-pass exponent, by contrast, could be below the world record, still working on filling in lower exponents that have not yet been tested.

Currently, the lowest exponent without an LL test is in the vicinity of 36M; however the largest known Mersenne prime is M43112609. See http://www.mersenne.org/primenet/ for a detailed breakdown; any of the numbers in the "LLERR" and "NO-LL" columns between 36M and 43M are fair game for "Smallest available first-time tests" but not "World record tests".

Note that many of the exponents in those "holes" below 43112609 are currently assigned, so the lowest available unassigned number at any given moment may be greater than the world record, in which case the two options will be identical. The main difference is that WRT is guaranteed to give you something bigger than the world record.

One minor exception:

While a "World record tests" exponent is greater than that of the largest known Mersenne prime at the time the assignment is made, this does not mean that it's "guaranteed to be a world record if if it turns up prime" or "guaranteed to give you something bigger than the world record"!

Why?

A new world record may have been set with a larger exponent than yours, by someone else, while you were testing your exponent. This circumstance is unlikely, but it is possible.

[Rodrigo]

Originally Posted by cheesehead

A new world record may have been set with a larger exponent than yours, by someone else, while you were testing your exponent. This circumstance is unlikely, but it is possible.

cheesehead,

That makes sense, thanks.

Rodrigo

[cheesehead]

Originally Posted by Rodrigo

For example, except for your patient explanation I wouldn't have known that "first-time tests" are the same as "smallest available first-time tests," or that "trial factoring to low limits" is the same as "TF-LMH." Surely there are other folks out there scratching their heads, but too embarrassed to ask?

Rodrigo

Just a note: GIMPS software messages were not all created in concert, at the same time. As the project has evolved, terminology that was clear in one place has sometimes been rendered ambiguous by additional ranges or functions added elsewhere years later.

GIMPS is a volunteer effort. If you really, really want to see some change made, get the source code, figure out what to change, test it on your own system, then send George Woltman a before/after/changes/documentation/test-case-results listing for the affected parts. :-) Or at least do the part about figuring out all the source code, file content and documentation changes.

[Rodrigo]

cheesehead,

Well, I'm not a programmer, so that rules out the source code part.

Procedurally speaking, how would one go about suggesting changes to the labels for the various work types so that they match? And, which set of labels (the manual assignments web page or the Prime95 Worker Windows menu) would you say is the "more" accurate or up to date?

Of course, now that I know what the labels mean, from my perspective there's less of a need to standardize them. But I gotta think that this has puzzled other folks, too, and maybe even deterred some of them from participating or continuing to participate in GIMPS, as they wonder what's what.

Now, from a purely selfish standpoint, that would suit me just fine as it means less competition for the awards , but I don't think that way. At least not ALL of the time...

As a pretty recent newcomer I'm keenly aware of the steep learning curve involved, and anything that would tend to reduce it is bound to help the overall project in terms of the number of participants. I suspect that it might be helpful to newcomers to have more uniform naming of the various work types across the board, although I'm not sure that I'd be the most qualified person either to put the idea into a detailed proposal (see three paragraphs above) or to actually carry it out (see four paragraphs above).

But I'd be happy to put together a list of pages across the various web sites and pages where the labels might be able to use some standardization. Of course, the first question would be which set of labels to use as a starting point (the Manual Assignments page or the Worker Windows menu), and that decision might hinge on practical issues (such as, which one is easier to change) as much as on issues of "up-to-dateness."

One last thing: If folks who are already in the know consider that this would be too much effort for the potential benefit, or if they prefer not to tinker with things as they are, I can go along with that too. I'm not trying to make waves here...

Just my $0.02. Thanks for explaining about the evolution of the project, that too makes a lot of sense.

Rodrigo

[TimSorbet]

Originally Posted by cheesehead

GIMPS is a volunteer effort. If you really, really want to see some change made, get the source code, figure out what to change, test it on your own system, then send George Woltman a before/after/changes/documentation/test-case-results listing for the affected parts. :-) Or at least do the part about figuring out all the source code, file content and documentation changes.

Well yeah, but it's not unreasonable to request that the ones in charge make the change, especially when it's a simple text change like this, and not something like a major feature or rewrite. Especially since you can't edit the source of PrimeNet.
When you start talking about making real changes to the workings of the program, sure it's good to have an idea of the source code and even suggest what needs to be changed.

[cheesehead]

You're both right.

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.