Awfully small factors....

[petrw1]

Originally Posted by S485122

Higher than the first factors found.

For the exponent I cited you can clearly see a 35 bits factor found in October 2007 and three LARGER factors found by Gareth (they may be larger but are still small at 36, 44 and 63 bits.) The 36 and 44 bits factors certainly qualify as awfully small factors for ranges that have already been factored to 63 bits.

Jacob

So what am I not understanding?
The factoring limits reports show all ranges to at least 59 bits.
I thought TF was 100% effective at finding factors.
If so there should not be any more to find below that bit level.

[S485122]

Originally Posted by petrw1

So what am I not understanding?
The factoring limits reports show all ranges to at least 59 bits.
I thought TF was 100% effective at finding factors.
If so there should not be any more to find below that bit level.

Because once a factor is found at bit level 28 for instance (the smallest possible factors for the 128M range of exponents) the search is STOPPED. This means that if a range has a status of factored to 63 bits, all the exponents in that range have been tested for 28 bit factors, those for which no factor was found will be tested for 29 bit factors, and so on... But if a 28 bit factor has been found it does not imply that there are not OTHER (and larger) factors. Gareth takes a bunch of already factored exponents and looks for larger factors than those already found. Look at the example I gave :

Exponent  | Date found       | Bits | Factor
128557967 | 2007-10-08 14:14 | 35   | 31882375817
128557967 | 2009-11-19 02:11 | 36   | 58879548887
128557967 | 2009-11-19 02:11 | 44   | 10081001540273
128557967 | 2009-11-19 02:11 | 63   | 5171044349132734223

It all concerns the SAME exponent.

Jacob

[petrw1]

Originally Posted by S485122

Because once a factor is found at bit level 28 for instance (the smallest possible factors for the 128M range of exponents) the search is STOPPED. Gareth takes a bunch of already factored exponents and looks for larger factors than those already found.
Jacob

Okay I understand that.
So if Prime95 stops after a factor is found then is Gareth using a different program or using Prime95 in some different way to get the extra, missing factors at these low bit levels?

[S485122]

Originally Posted by petrw1

So if Prime95 stops after a factor is found then is Gareth using a different program or using Prime95 in some different way to get the extra, missing factors at these low bit levels?

Exactly. Once he finds all (if the undocumented option SendAllFactorData had been used) factors at bit level "b", he starts a new workunit :

Factor=exponent,b+1,63

It can be 63 or any bit level he wants.

Jacob

[Prime95]

Originally Posted by petrw1

So if Prime95 stops after a factor is found then is Gareth using a different program?

Yes, he is using a different program.

[Graff]

Originally Posted by petrw1

Some recently turned in Manual Testing factors are under 40 bits???

GrunwalderGIMP       Manual testing   128557967 F        Nov 19 2009  2:11AM   0.0   0.0000  58879548887                                  
GrunwalderGIMP       Manual testing   128556863 F        Nov 19 2009  2:11AM   0.0   0.0000  46280470681 
GrunwalderGIMP       Manual testing   128556803 F        Nov 19 2009  2:11AM   0.0   0.0000  762341841791

and many more at that time....

They are listed, valid factors but how is it that such small factors are being turned in now? This range was likely factored to that level a 'long' time ago.

Wasn't able to respond to this earlier as I was at work and I can't
remember my forum password!

As noted in a thread in the LMH section, I use a port of Peter
Montgomery's MFactor on a number of Alpha workstations. This program
is limited to factoring expinents up to 2^27 in size up to 2^63. In the
recent past I used this to do first factor searching, but since most
exponents below 2^27 are now at 2^63 (or beyond), I shifted my focus
back to my original use of MFactor which was/is additional factor
searching.

I simply look for exponents where the largest known factor is < 2^63.
For each such exponent found, I run a search up to 2^63. It's
actually quite productive, although it gets very little credit in the
rankings. I have two runs going at the moments, 128M on the
smaller setup and 127M just restarted on the larger setup.

Gareth (GrunwalderGIMP)

[petrw1]

Originally Posted by Graff

Wasn't able to respond to this earlier as I was at work and I can't
remember my forum password!

As noted in a thread in the LMH section, I use a port of Peter
Montgomery's MFactor on a number of Alpha workstations. This program
is limited to factoring expinents up to 2^27 in size up to 2^63. In the
recent past I used this to do first factor searching, but since most
exponents below 2^27 are now at 2^63 (or beyond), I shifted my focus
back to my original use of MFactor which was/is additional factor
searching.

I simply look for exponents where the largest known factor is < 2^63.
For each such exponent found, I run a search up to 2^63. It's
actually quite productive, although it gets very little credit in the
rankings. I have two runs going at the moments, 128M on the
smaller setup and 127M just restarted on the larger setup.

Gareth (GrunwalderGIMP)

Thanks for clearing this up and hope I don't cause too much excitement.