P-1 factoring anyone?

[Kevin]

Originally Posted by Primeinator

Is this not desirable, though? Looking at the overall status (exponents to one billion), it is apparent that hundreds of thousands of potential candidates have been factored (those far above 50M even), presumably by trial factoring though I may be mistaken on this.

What difference does it make if that trial factoring is done now or in 5 years? Each work-type just needs to produce enough to feed the next step in the process. Trial factoring is producing far more than it needs to keep up with P-1, and P-1 isn't producing enough to keep up with LL. Nobody's really waiting on double checks, but I feel the gap between first and second time tests is getting uncomfortably large, leaving a lot of exponents with possible faulty LL tests in limbo. At this point, isn't the leading edge of LL around 50M, with the leading edge of LL-D around 21M? I wouldn't be surprised if somebody could heuristically show using the number of singly tested exponents/error rate of LL tests/"probability" of success that there's a good chance we've missed a prime.

[cheesehead]

Originally Posted by Primeinator

Is this not desirable, though? Looking at the overall status (exponents to one billion), it is apparent that hundreds of thousands of potential candidates have been factored (those far above 50M even), presumably by trial factoring though I may be mistaken on this.

Yes, but most factors found by TF are rapidly found at low limits. Each time TF goes up one bit level, it's twice (or more) as expensive for finding the (approximately) same number of factors. Most TF factor-finding happens swiftly at low levels and easily races ahead (in exponents assigned) of P-1, which never finds factors as rapidly as TF, so P-1 is where we're short of CPU contribution, not TF.

[lfm]

I have a core on P-1 and it seems to get assignments in the 50m exponent range. Th first time LLs seem to be currently in the 44m - 45m range. If Most of the LLs have not had P-1 done why aren't they closer together?

[garo]

Yes it is clear to me that P-1 is not keeping up. We need more people to do P-1. I have dedicated half my resources to P-1.

lfm, the reason for that is that P-1 should optimally be done before the last bit of TF. So P-1 at 50M is a bottleneck for the last bit of TF for the exponents in that range. Exponents in the 45-49M range have already been completely TFed. So George made the call to start P-1 on the v5 server at the 50M range. If you wish, you can select unassigned exponents in lower ranges to do P-1 on. I had about 50 exponents assigned to me near 46-47M that have been fully TFed but not had P-1 done. You will need to use the server forms and create worktodo lines yourself for that.

PS: I moved 9 posts from the other thread http://www.mersenneforum.org/showthread.php?t=12156 to this one as the discussion is more relevant here. We'll leave markr's thread for P-1 on small exponents.

[lfm]

Originally Posted by garo

Yes it is clear to me that P-1 is not keeping up. We need more people to do P-1. I have dedicated half my resources to P-1.

lfm, the reason for that is that P-1 should optimally be done before the last bit of TF. So P-1 at 50M is a bottleneck for the last bit of TF for the exponents in that range. Exponents in the 45-49M range have already been completely TFed. So George made the call to start P-1 on the v5 server at the 50M range. If you wish, you can select unassigned exponents in lower ranges to do P-1 on. I had about 50 exponents assigned to me near 46-47M that have been fully TFed but not had P-1 done. You will need to use the server forms and create worktodo lines yourself for that.

By "create worktodo lines yourself for that" you mean that not even manual assignment will help? Cuz I tried manual assignment of P-1 in the 46M to 49M range and it said there was none available! It gave me some doublechecks. The primenet summary report sez there is over 50,000 available ATM. I guess the server or the report is kinda confused cuz the final TF passes were done before the P-1.

I just want to do what GW and you, Garo have asked, to help the first time LLs by doing some of the P-1 for them. The 50m range seems a bit far out in the future and less urgent than indicated. Maybe I am missing something or maybe you guys are taking a longer term view.

[Primeinator]

I do not think it will take long for first time LLs to be hitting the 50M range. Most of mine recently have been around 45M but one of mine, now at 70% or so, is in the 48M range. Historically, how often does P-1 (stage 1 or 2) find a factor?

[Kevin]

Originally Posted by Primeinator

I do not think it will take long for first time LLs to be hitting the 50M range. Most of mine recently have been around 45M but one of mine, now at 70% or so, is in the 48M range. Historically, how often does P-1 (stage 1 or 2) find a factor?

Assuming you use a reasonable amount of memory, about 6-7% of the time.

[Work thread Jul 16 08:03] Optimal P-1 factoring of M50994199 using up to 1024MB of memory.
[Work thread Jul 16 08:03] Assuming no factors below 2^68 and 2 primality tests saved if a factor is found.
[Work thread Jul 16 08:03] Optimal bounds are B1=600000, B2=16650000
[Work thread Jul 16 08:03] Chance of finding a factor is an estimated 6.68%

[Primeinator]

That's kind of what I thought. Unfortunately, this does not increase much if you were give it a lot more memory. Such as 4 gigs instead of 1...it makes a very small difference.

[petrw1]

Originally Posted by lfm

Cuz I tried manual assignment of P-1 in the 46M to 49M range and it said there was none available!

Check out post #180 from George....this is intentional.

[garo]

lfm, it is best for the project if you do P-1 in the 50M range. We should be getting to that range in a few months and if George has opened that range up you can assume he wants that range to be done first.

[cheesehead]

Originally Posted by lfm

Maybe I am missing something or maybe you guys are taking a longer term view.

A bit of both: we veterans know more of the history as to why and when certain things happened and what the reasons were.

You're looking at the results of an ongoing historical process, not a constant algorithm that's always been in effect since the beginning of GIMPS.

I guess the server or the report is kinda confused cuz the final TF passes were done before the P-1.

No confusion. The server and its parameters have been changing (for the better) over time. It used to be standard to do all TF before any P-1.

When P-1 factoring ability was first added to prime95/mprime, the server refinement about doing P-1 before the last level or two of TF was not included. Only later were the benefits of that quantified. Because the benefits were small compared to other possible improvements to GIMPS, development of the ability for the server to make separate P-1 assignments, and to do so before the final level(s) of TF, had a low priority. So it's only recently that that's been added.

I just want to do what GW and you, Garo have asked, to help the first time LLs by doing some of the P-1 for them. The 50m range seems a bit far out in the future and less urgent than indicated.

In a few years, you'll have acquired all our veteran wisdom. :)

But please keep asking questions. We need those both to spur us to document our "wisdom", and to point out its flaws.