20161217, 08:53  #34  
Sep 2003
101000011100_{2} Posts 
Quote:


20161219, 21:52  #35  
Sep 2002
Oeiras, Portugal
2655_{8} Posts 
Quote:
User kkmrkkblmbrbk (!!!)  gosh, is that really you?...  has found a new one in the 40K range. Well done! Last fiddled with by lycorn on 20161219 at 21:54 

20161219, 22:48  #36 
1976 Toyota Corona years forever!
"Wayne"
Nov 2006
Saskatchewan, Canada
3×29×53 Posts 
If I read it right we (not me....the other we) found 5 sub20K 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 20161219 at 22:51 Reason: Cleaner URLs 
20161220, 19:38  #37  
Sep 2003
2^{2}×647 Posts 
Quote:
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. 

20170131, 16:46  #38  
Sep 2008
Masontown, PA
2×19 Posts 
THANK YOU GENIUSES!!!
Quote:
Second, I have refocused my meager efforts to attempt to find firstfactors for sub20k exponents. Good luck to us all! Third, I am completely honored by and to GP2 (kkmrkkblmbrbk) !!! Congratulations to you on all of your firstfactor finds and your MASSIVE amount of effort! Fourth, for anyone interested, M1277 is 2601983048666099770481310081841021384653815561816676201329778087600902014918340074503059860433081046210605403488570251947845891562080866227034976651419330190731032377347305086443295837415395887618239855136922452802923419286887119716740625346109565072933087221327790207134604146257063901166556207972729700461767055550785130256674608872183239507219512717434046725178680177638925792182271 

20170201, 03:26  #39 
Sep 2003
2588_{10} Posts 
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 supersmooth 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. 
20170209, 19:25  #40  
Sep 2008
Masontown, PA
2×19 Posts 
Congratulations and thank you again!
Quote:
If I may ask petrw1 a followup question about his post, is there something "special" about the sub20K 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 morequickly, 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! 

20170209, 20:23  #41 
"Curtis"
Feb 2005
Riverside, CA
47×101 Posts 
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!

20170209, 20:53  #42  
Sep 2008
Masontown, PA
2·19 Posts 
So much intelligence!
Quote:
I was speaking of ECM effort, my apologies for being ambiguous and shortsighted. I wish I knew more about so much of this so that, at the very least, I could make much moreintelligent 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 userfriendly 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 P1 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. 

20170209, 21:58  #43  
Sep 2003
2^{2}·647 Posts 
Quote:
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 

20170209, 23:11  #44  
"Curtis"
Feb 2005
Riverside, CA
47×101 Posts 
Quote:
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. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Modular restrictions on factors of Mersenne numbers  siegert81  Math  23  20140318 11:50 
Mersenne prime factors of very large numbers  devarajkandadai  Miscellaneous Math  15  20120529 13:18 
Factors of Mersenne Numbers  asdf  Math  17  20040724 14:00 
Factoring Smallest Fermat Numbers  Erasmus  Factoring  32  20040227 11:41 
Factors of Mersenne numbers ?  Fusion_power  Math  13  20031028 20:52 