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Old 2010-10-27, 10:12   #1
schickel
 
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Question Open discussion: whither the project?

I have been asked in a couple of PMs what the next project is going to be now that the "easy" work of taking sequences under 1 million up to 100 digits.

As far as the "take a sequence to 100 digits" part of it goes, that is almost at an end. The only remaining range that hasn't been taken to 100 digits and uploaded to the DB between 1 and 1,000,000 is Wieb Bosma's range from 250,000-450,000. For those of you joining late, this range has been completed from 250,000 up through 430,000, but the results have not been made public by Wieb. I emailed him about our project when we were awarded the sub-forum, but never recieved an answer. kar_bon contacted him after the FatorDB was set up to handle aliquot sequences, and also got word from Wolfgang that he is/was willing to provide his data; but I just checked a couple of sequences and as far as I can tell, they have not been uploaded to the DB yet. That means that one possible project would be to check Wieb's tables, check the DB and take sequences that haven't been uploaded to the DB to 100 digits or more. This would be a viable project for newcomers to the project to be able to see how things work without having to tackle 100+ digit factorizations right from the get-go. It would, of course, be rendered moot when Wieb does release his results.

Another possible project would be to find another sequence <10,000 (or 100,000) to take up as a team project. 4788 is of particular interest since its side sequence (314718) is how the longest sequence at >9,000 lines. If we could find something else, either another long sequence pair or a longer (more than 28 steps) or higher (50 or 60 digits) aliquot cycle, that would be interesting.

Another possibility would be to pick something like a dozen sequences and advance them by team ECM and/or GNFS as required. This would provide a nicer mix of work, with some NFS jobs easily doable as solo jobs until they got above 130-140 digits.

Another possibility is to just settle down as a project that provides mildly interesting composites in a range of sizes to people that become interested in factoring for whatever reason and want to try it for themselves.

Another possibility is to just keep on extending from 1M upward on into the future. A drawback to this is that as we go higher and higher, the job of keeping track of this becomes harder and harder. (And we just end up with more and more sequences that don't terminate. It might be more interesting to see if we could manage to terminate any more "low" sequences....)

Unfortunately, since all the "low-hanging" fruit has been plucked, the real work of taking sequences from their current size to termination or driver contol has moved into the realm where real dedication is required. As an indication of the time required: for those that didn't read all the way through all the threads, here is my release of a sequence that got as high as 135 digits before capturing a driver. I spent almost 2 years working on this one.

So what do you all think? Does this project have a future here on Mersenneforum or will it whither on the vine? I know that for me, this is my project of choice. When I started factoring I bounced around and participated in several projects, but now it's been 4 years and I'm (apparently) hooked on sequences.....
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Old 2010-10-27, 10:22   #2
fivemack
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I agree that aliquot sequences provide a variable-rate drip-feed of results which make them quite appealing. I've been dealing with about eight <10k sequences for the better part of two years now, with a couple of 160-digit GNFS runs and a fair number of C150+ ones, though I suppose I have fairly large compute resources.

I don't see that hundred-digit factorisations are a problem: they only mean that collaborators have to have working GGNFS installations, even 110 digits is about twelve hours on one core2 core.
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Old 2010-10-27, 18:10   #3
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Checking the DB, at least some of Wieb's range is in there - I think I remember someone rerunning part of it a while ago, but I can't remember who it was.

Personally, like fivemack, I don't see why taking sequences to 110 digits should be too difficult for most people.
As for the other options, I would like to see the (very) old aliquot cycle record broken. That is most likely to happen if we go on above 1M and stop computations relatively low. However, there will then be less interest in the actual sequences.
If doing long jobs is the problem (and it doesn't look like it should be), then starting a team effort on another high sequence, or working on a small number of sequences as a group, doesn't seem like a good idea.
Neither does doing the same thing over and over again, which is what we're currently doing. As we move up towards 1M the number of terminations in the 110 digit efforts should increase due to less work having been done on the higher sequences. Still, if terminations are what attract people to the project, maybe going above 1M is the thing to do.
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Old 2010-11-06, 07:26   #4
schickel
 
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Based on the level of participation in this discussion so far, I see the project splintering into several different sub-groups:
  • A small core of dedicated people willing and able to run sequences to high levels. Takes a great deal of commitment and maybe a lot of resources.
  • A small group of people willing to run sequences if they're "easy". The only "big" jobs required would be <=110 digits. No great commitment in time or effort required. Only problem here: not much left <1 million; interesting sequences will most likely be run by the group 1 participants as they crop up during individual work on "hard" sequences.
  • Someone dumping a large number of sequences in to the DB (probably >1 million based on the way things have looked in the DB for a week or so). This effort will be uncoordinated unless someone is willing to take on the task of allocating and tracking the sequences in some reasonable sized blocks (10K, 100K, ??) This would be aided by development of an automated tool to find the sequences that don't terminate right away. One severe consequence I see is that the DB could be turned into a bot to extend sequences as the number of small sequences that will extend "easily" using just the DB resources increases.*
I hope that there will be enough people doing enough different work that the sub-forum here will remain active, though almost certainly with a very much lower message volume.

Quote:
Originally Posted by 10metreh View Post
As for the other options, I would like to see the (very) old aliquot cycle record broken. That is most likely to happen if we go on above 1M and stop computations relatively low.
Probably the better option, then, would be to do an exhaustive search rather than just extend sequences to see if one cycles, since, as of '07 anyway, the search had been extended up to 14 or 15 digits....
Quote:
Originally Posted by 10metreh View Post
However, there will then be less interest in the actual sequences.
You're correct there.
Quote:
Originally Posted by 10metreh View Post
If doing long jobs is the problem (and it doesn't look like it should be), then starting a team effort on another high sequence, or working on a small number of sequences as a group, doesn't seem like a good idea.
Neither does doing the same thing over and over again, which is what we're currently doing.
Well, if doing the same thing over and over were a propblem, none of us would have started working on this project. The very definition of this project is a long series of very boring factorizations that may result in an end to a particular sequence....

I think another team sequence might actaully be a good thing, since we could have ECM effort running while sieving and post-processing on other seuences is running. The problem here would be to find another sequence that would be worth pursuing. Different kinds of work available here: finding another sequence with no driver at a very high level or taking the longer sequences as high as possible trying for record length.
Quote:
Originally Posted by 10metreh View Post
Still, if terminations are what attract people to the project, maybe going above 1M is the thing to do.
In that case, the termination tracking should be broken into at least two seqments, since sequences that terminate after reaching heights of :hand waving: <50 digits, say, are certainly very much less "interesting" than sequences that reach even 80 digits.... And any terminations of sequences <100K would certainly be the most interesting of all.

-----------------------------

My thought is that even if activity slows down here, several advances have come from all the effort here. Aliqueit from Mikael Klasson is certainly the second most exciting thing to come out of this project. It is so far beyond the UBASIC program that they're not even in the same league.... The most exciting thing would seem to be the integration of aliquot sequences into the factoring DB (one central repository makes collecting and tracking results entirely painless), followed closely by the surge of interest in sequences in general; since Wolfgang had put his project on hiatus there were very few people working on sequences.

=======================

[b]*[/b]It looks like it may have settled down a little, but if you looked at the "smallest composites" page, all the ones <70 digits for the last week or so looked to be part of an aliquot sequece if you followed the "more info" link for the individual composites.
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Old 2010-11-06, 21:47   #5
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If one wants to find a longer cycle, I think we should search 1-5 million sequences to 80 digits. We already know that the largest term has to be over 14-15 digits so aliqueit could be run to say 12-15 digits to remove all numbers that have no chance. Once we have that list, rather than reserving single numbers, I would think one would reserve a 1k or 5k range, with some kind of file to tell the user which numbers to test.

The user then runs all numbers in a file up to 80 digits.

Numbers smaller than 10^14 for example can be found by using a list of prime numbers to 10 million and simple division using 64 bit long integers so you don't need aliqueit to do it.
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Old 2010-11-08, 00:51   #6
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Quote:
Originally Posted by schickel View Post
So what do you all think? Does this project have a future here on Mersenneforum or will it whither on the vine? I know that for me, this is my project of choice. When I started factoring I bounced around and participated in several projects, but now it's been 4 years and I'm (apparently) hooked on sequences.....
You can search also for sociable numbers, the known exhaustive search limit is "only" 4*10^12 (or 5*10^12 ?). Raising it to say 2*10^13 wouldn't take much long time. There are some tricks to lower the number of factorizations, say searching solutions in [5*10^12,10^13] interval where the largest term is below 10^13 requires factoring less than 10^12 numbers.

The probability of success is high to find a new sociable number.
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Old 2010-12-06, 20:35   #7
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After completing the majority of a complete survey recently, I can see several more types of subproject that could be opened.

One, there are numerous sequences that are at 100 digits or more but are not under driver control. So we could start a project based on individual sequences rather than a particular range. The goal would be to advance a sequence until a driver was obtained or it became unmanageable. (I am almost to that point with 363270: it's at 161 with a c155 I am currently gnawing away at...)

Two, we could take one or two of the longer sequences, driver controlled or not, and see how far we could extend them....

And three, we could take the shortest sequences and extend them all to, say, 500 lines, although this would probably be incredibly hard, since the ones that make 100 digits in under 500 lines usually have 2^3 * 3 * 5 as the driver from the beginning....which tends to make a sequence grow by a digits every 3 or 4 lines. (I was going to say 1000, but looking at just the 600k range, the 5 shortest sequences are all <300 lines long....)
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Old 2010-12-08, 16:52   #8
henryzz
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It might be nice to take driverless sequences to 120 digits or to a driver >110 digits. Maybe sequences with a 3 should just be taken to 115, but that would complicate things.
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Old 2010-12-09, 09:35   #9
schickel
 
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Quote:
Originally Posted by henryzz View Post
It might be nice to take driverless sequences to 120 digits or to a driver >110 digits. Maybe sequences with a 3 should just be taken to 115, but that would complicate things.
Should we make this a sub-project? Now that we've got a full round up of everything, the driverless ones are going to be easy to find...
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Old 2010-12-11, 09:59   #10
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Quote:
Originally Posted by schickel View Post
Should we make this a sub-project? Now that we've got a full round up of everything, the driverless ones are going to be easy to find...
Might be an idea. We could follow on the tail of the to 110 digits subprojects.
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