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Old 2016-12-17, 08:53   #34
GP2
 
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Even though I'm working on these myself, I'm somewhat pessimistic. I think Bob Silverman was of the opinion that it was more useful to throw more ECM at them instead of taking P−1 to very high levels. Recall that some factors are basically invisible to P−1 (the ones that happen to have non-smooth k). I'm finding a bunch of second, third and higher factors, but any exponents that still have no known factors have already been tested with ECM to a pretty large depth without success.
Well maybe there's some hope. I've now found first factors for two exponents in the 30K range (M33871 and M39409), those were 38-digit and 42-digit factors respectively. But in the 10K range it would have to be at least a 45+ or 50+ digit factor, given the amount of ECM that's been done. I guess we'll see.
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Old 2016-12-19, 21:52   #35
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I've now found first factors for two exponents in the 30K range (M33871 and M39409),
And I think you´ve done it again...
User kkmrkkblmbrbk (!!!) - gosh, is that really you?... - has found a new one in the 40K range. Well done!

Last fiddled with by lycorn on 2016-12-19 at 21:54
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Old 2016-12-19, 22:48   #36
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Default If I read it right we (not me....the other we) found 5 sub-20K in 2016.

Can we (this time including me) find another 5 in 2017?

3607
5879
5923
6329
15149

20K is the limit below factoring is not easily supported.

Last fiddled with by petrw1 on 2016-12-19 at 22:51 Reason: Cleaner URLs
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Old 2016-12-20, 19:38   #37
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And I think you´ve done it again...
User kkmrkkblmbrbk (!!!) - gosh, is that really you?... - has found a new one in the 40K range. Well done!
Yeah, 42349. But all three of these factors have very specific characteristics: they have a number of digits at least in the high 30's or low 40's and they have super-smooth k.

So P−1 can find such factors more efficiently than ECM, but factors of this form are rare. So after it finds a handful, there probably won't be any more left to find by using P−1. We'll see.
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Old 2017-01-31, 16:46   #38
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Smile THANK YOU GENIUSES!!!

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Originally Posted by petrw1 View Post
Can we (this time including me) find another 5 in 2017?

3607
5879
5923
6329
15149

20K is the limit below factoring is not easily supported.
First, THANK YOU to everyone who has contributed to this thread! I very much appreciate your knowledge and kindness!

Second, I have refocused my meager efforts to attempt to find first-factors for sub-20k exponents. Good luck to us all!

Third, I am completely honored by and to GP2 (kkmrkkblmbrbk) !!! Congratulations to you on all of your first-factor finds and your MASSIVE amount of effort!

Fourth, for anyone interested, M1277 is 2601983048666099770481310081841021384653815561816676201329778087600902014918340074503059860433081046210605403488570251947845891562080866227034976651419330190731032377347305086443295837415395887618239855136922452802923419286887119716740625346109565072933087221327790207134604146257063901166556207972729700461767055550785130256674608872183239507219512717434046725178680177638925792182271
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Old 2017-02-01, 03:26   #39
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Thanks, you're much too kind.

I did find one other first factor for a smallish exponent recently, namely M52999. It fits the same rare pattern as the previous ones: it's 41 digits and has super-smooth k = 7 × 151 × 98947 × 63544739 × 669520493 × 62882930057. Also found a few first factors in the 200K range, where the prior searches have been a bit less thorough.
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Old 2017-02-09, 19:25   #40
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Thumbs up Congratulations and thank you again!

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Originally Posted by GP2 View Post
Thanks, you're much too kind.

I did find one other first factor for a smallish exponent recently, namely M52999. It fits the same rare pattern as the previous ones: it's 41 digits and has super-smooth k = 7 × 151 × 98947 × 63544739 × 669520493 × 62882930057. Also found a few first factors in the 200K range, where the prior searches have been a bit less thorough.
Congratulations, GP2, on all of your finds, both first factors and all of the larger factors you are finding in the sub-100K range! I'd love to know how many CPUs you are using, but I understand if you do not want to tell.

If I may ask petrw1 a follow-up question about his post, is there something "special" about the sub-20K range that merits extra searching, or is it just worth working on because it is difficult and rare? Assuredly there are higher exponents that can be worked on more-quickly, but maybe it is a better use of our time and effort to look at smaller exponents? Just curious what your opinions are.

Since M1277 is 385 digits long, a factor can be as big as 192 digits long, so I doubt we'll ever find it, even with the awesome attempts Lycorn is making at it. What do you geniuses think?

Thank you all again!
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Old 2017-02-09, 20:23   #41
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Originally Posted by UberNumberGeek View Post
Since M1277 is 385 digits long, a factor can be as big as 192 digits long, so I doubt we'll ever find it, even with the awesome attempts Lycorn is making at it. What do you geniuses think?

Thank you all again!
M1277 is within SNFS range now, so I have no doubt we'll have factors for it; I bet it'll be factored by yearend 2020. If you meant to ask whether we'll ever factor it via ECM, odds are decreasing rapidly as we near t65 effort complete. There's something like a 15% chance of a factor turning up between now and the completion of a t75, which would be a monumental amount of ECM!
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Old 2017-02-09, 20:53   #42
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Thumbs up So much intelligence!

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Originally Posted by VBCurtis View Post
M1277 is within SNFS range now, so I have no doubt we'll have factors for it; I bet it'll be factored by yearend 2020. If you meant to ask whether we'll ever factor it via ECM, odds are decreasing rapidly as we near t65 effort complete. There's something like a 15% chance of a factor turning up between now and the completion of a t75, which would be a monumental amount of ECM!
VBCurtis, it is also a sincere honor to hear more from you, thank you!

I was speaking of ECM effort, my apologies for being ambiguous and short-sighted. I wish I knew more about so much of this so that, at the very least, I could make much more-intelligent statements and questions. Thank you for being kind, VBCurtis.

I am not familiar, of course and obviously, with SNFS, SNFS@home, BOINC, or anything that is not Prime95. Does anyone on here know if SNFS@home is as user-friendly as Prime95? More specifically, does anyone know if SNFS@home would allow me/us to "cherry pick" M1277 to try to factor it? I apologize for both not knowing and for asking those of you out there to do the legwork for me.

It would be great if someone knew, or it was listed somewhere, when to stop/start using P-1 based upon ECM, and then when to start to try SNFS. I only have 4 computers at my disposal, and two are work machines, for which I have permission to use Prime95 on them, but ONLY Prime95. I just hate wasting my time and the time of you geniuses here in the forum. Again, my thanks to all for being kind and helpful.
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Old 2017-02-09, 21:58   #43
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Congratulations, GP2, on all of your finds, both first factors and all of the larger factors you are finding in the sub-100K range! I'd love to know how many CPUs you are using, but I understand if you do not want to tell.
It varies. I have about 8 cores with high memory doing P−1 stage 2. I would use more, but the need for lots of memory is a constraint. I used a bunch of cores with low memory to do P−1 stage 1 earlier and still have a few doing that.

I also have about 20 cores doing ECM, which doesn't need much memory at all and is probably a more promising approach than P−1, in hindsight.

Found one more first factor, M56843
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Old 2017-02-09, 23:11   #44
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Originally Posted by UberNumberGeek View Post
I am not familiar, of course and obviously, with SNFS, SNFS@home, BOINC, or anything that is not Prime95. Does anyone on here know if SNFS@home is as user-friendly as Prime95? More specifically, does anyone know if SNFS@home would allow me/us to "cherry pick" M1277 to try to factor it? I apologize for both not knowing and for asking those of you out there to do the legwork for me.

It would be great if someone knew, or it was listed somewhere, when to stop/start using P-1 based upon ECM, and then when to start to try SNFS. I only have 4 computers at my disposal, and two are work machines, for which I have permission to use Prime95 on them, but ONLY Prime95. I just hate wasting my time and the time of you geniuses here in the forum. Again, my thanks to all for being kind and helpful.
NFS@Home has not yet shown interest in M1277. When I said "it is within SNFS range", I was being optimistic; the parts of the SNFS effort that are easily shared among many machines can be attempted now, but the part that must be done on a single cluster needs, well, a cluster. That matrix-solving step would take something over a year on a 48-core machine; the sorts of people with those resources are also the sorts who just do the entire factorization themselves without public assistance.

As for an estimate of when to give up ECM and move to SNFS, one rule of thumb is 0.21 of the difficulty of the number. I think M1277 is 385 digits; 0.21 * 385 is around 80 digits' worth of ECM. A t80 is about 6*t75, ~30*t70. We're in the t65 range, so ECM is definitely the plan for quite a while longer still; we've done perhaps 1% of the ECM we should do! This "rule of thumb" is used for smaller projects widely (0.21 or 0.22), but is *not* accurate for any size of project; I don't know if a t80 is actually a good plan for M1277, or if something on the order of half that effort is enough to give up on ECM and wait for a Cluster Owner to agree to help out with SNFS.
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