Factoring database

[kar_bon]

all factorizations above 90 digits have to be done manually by msieve.
Markus (Syd) implemented this border, so his workers will not be occupied by such amount of work.
all work for this number you have done here, more work is not worth.

if i use the workers, i try about 3 or 4 times of the ECM levels each, then you can be sure there's no low factor missed.

[gd_barnes]

OK, thanks Karsten. That is basically what I tried...several hits on each of the ECM levels before giving up.

Can you provide me with a link to the latest msieve for Windows? A linux version would be OK but my "play around" machine is Windows. Although I've messed around with Alpertron's applet quite a bit, I'm mostly a newbie to the factoring arena. This database is very cool.

I just now had the same problem on that sequence with n=326 that has a 93-digit composite factor.

[kar_bon]

see this thread: http://www.mersenneforum.org/showthread.php?t=3255

i'm just sieving 2^317*2293-1!

[Mini-Geek]

I've noticed the Sieve and Very High Limits buttons disappear after a certain amount of work, too. (Edit: Ok, so Gary's issue is just that Sieve isn't allowed on large numbers, but my statements still stand) It doesn't make sense to me either, Gary. Is this by design Syd? I'd think if anything it should be just the opposite: after work at a certain level gets completed and practically eliminates the chance of finding a factor at a lower level, the lower levels should become unavailable. And, unless I'm misunderstanding something about the P-1 method, the P-1 button should disappear or switch to higher limits after a P-1 is run with equal or higher limits than what happens when you click that button. I think something similar with P+1 after 3-5 runs would be in order as well.

(similar to kar_bon's link...) Here are links to download compiled versions of several good factoring programs:
http://gilchrist.ca/jeff/factoring/
As kar_bon implied, numbers of this size are easily done by a single computer with a little patience. Using the SIQS method with YAFU or Msieve (they're about as fast, you could do some testing to see which is faster on your CPU, for mine it's YAFU) would probably be the best option for a number this size.

[henryzz]

try http://factorization.ath.cx/workerstatus.php
for explanations of what the limits are

[gd_barnes]

Originally Posted by Mini-Geek

I've noticed the Sieve and Very High Limits buttons disappear after a certain amount of work, too. (Edit: Ok, so Gary's issue is just that Sieve isn't allowed on large numbers, but my statements still stand) It doesn't make sense to me either, Gary. Is this by design Syd? I'd think if anything it should be just the opposite: after work at a certain level gets completed and practically eliminates the chance of finding a factor at a lower level, the lower levels should become unavailable. And, unless I'm misunderstanding something about the P-1 method, the P-1 button should disappear or switch to higher limits after a P-1 is run with equal or higher limits than what happens when you click that button. I think something similar with P+1 after 3-5 runs would be in order as well.

(similar to kar_bon's link...) Here are links to download compiled versions of several good factoring programs:
http://gilchrist.ca/jeff/factoring/
As kar_bon implied, numbers of this size are easily done by a single computer with a little patience. Using the SIQS method with YAFU or Msieve (they're about as fast, you could do some testing to see which is faster on your CPU, for mine it's YAFU) would probably be the best option for a number this size.

Actually, my main issue is not that sieve disappears on larger numbers. It's that "ECM to very high limits" is not available on smaller numbers, i.e. about 87-95 digits. If it is available for a 100+-digit number, why is it not available for a 90-digit number? 90-digit numbers should take far less time to factor.

Syd, shouldn't smaller numbers take less time to factor and so shouldn't 'ECM to very high limits' be allowed on any number where a sieve is not allowed?

That said, I believe there is a much larger longer-range problem. From my experience, many of the factors currently in the queue for "ECM to very high limits" will take many CPU months to even years to find a factor. Am I correct on that? If so, there is a big slippery slope here. The last I looked, there are 27 numbers in the queue. I see there eventually being 100, then 200, then 300, etc. until there is such a queue of numbers that virtually none would ever get solved.

Perhaps the issue that I described is attempting to avoid the above long-range problem. Unfortunately it is the those large numbers that stack up in the 'ECM to very high limits" queue. I saw one last night for 307 digits, which (by my experience) may not get solved within a decade of CPU years. The smaller factors would likely get solved at some point.

Regardless, once again, this is an outstanding piece of work that, from what I can tell, has been needed for a long time.


Gary

[10metreh]

Originally Posted by gd_barnes

Actually, my main issue is not that sieve disappears on larger numbers. It's that "ECM to very high limits" is not available on smaller numbers, i.e. about 87-95 digits. If it is available for a 100+-digit number, why is it not available for a 90-digit number? 90-digit numbers should take far less time to factor.

I agree this could be a problem, but you can run the ECM yourself. It shouldn't take very long to do enough (about 200-250 curves at 25e4 for a 90-digit number), then sieving will only take about 3 hours on my P4 Willamette (much faster on Core 2 etc.)

That said, I believe there is a much larger longer-range problem. From my experience, many of the factors currently in the queue for "ECM to very high limits" will take many CPU months to even years to find a factor. Am I correct on that? If so, there is a big slippery slope here. The last I looked, there are 27 numbers in the queue. I see there eventually being 100, then 200, then 300, etc. until there is such a queue of numbers that virtually none would ever get solved.

Perhaps the issue that I described is attempting to avoid the above long-range problem. Unfortunately it is the those large numbers that stack up in the 'ECM to very high limits" queue. I saw one last night for 307 digits, which (by my experience) may not get solved within a decade of CPU years. The smaller factors would likely get solved at some point.

There could be small factors. Imagine spending several years factoring a C180 on your home computers, and a P30 appearing. So ECM must be run first. For the 307-digit number, if it is not of a special form, there is no way it could be factored now by GNFS. It would need to be ECM'ed to about 85-90 digits first. And doing VHL is a start

[henryzz]

Originally Posted by gd_barnes

Actually, my main issue is not that sieve disappears on larger numbers. It's that "ECM to very high limits" is not available on smaller numbers, i.e. about 87-95 digits. If it is available for a 100+-digit number, why is it not available for a 90-digit number? 90-digit numbers should take far less time to factor.

the reason it does that is because it is more efficient to factor those numbers by using QS or GNFS than by ecm
for example to run 30 digit ecm on a c60 would take 15 minutes and probably find a factor but the number could be definitely(forgetting bugs in the program and such like) factored by QS in 5 minutes
the reason that you cannot use the database to factorize numbers above c85 is that it would clog up the database by taking an hour or more each
VHL disappears when it is judged that the optimal amount of ecm has been done and it is time to move to QS or for >~c90 GNFS
we are actually rather lucky with the database it does more ecm than many people would recommend on small numbers

[10metreh]

Originally Posted by henryzz

we are actually rather lucky with the database it does more ecm than many people would recommend on small numbers

The t35 feature for c95-99s was quite nice. Although it was a bit excessive, a c99 should have (IMO) a bit more than t30.

[smh]

Originally Posted by 10metreh

... a c99 should have (IMO) a bit more than t30.

Which you can do yourself

[10metreh]

Originally Posted by smh

Which you can do yourself

Of course. I'm not asking Syd to add that. I am merely pointing out that using Syd's workers on a c99 no longer does a full test prior to GNFS.