20080718, 16:37  #23 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89×113 Posts 
Fresh from the oven. Very gratuitous:
(4ยท10^2071)/3 = 13333.......3333 <207 threes> = 227 ยท C205 = 227 ยท p100 ยท p106 p100 = 3999406295062729501331514001724671368377647689512510156551098073080765712556308639257272683646862107 p106 = 1468646766913267291096484238457962531138809604380942950365724174756132537097046980347507927618050634373797 Sergey Last fiddled with by Batalov on 20080718 at 16:41 
20080718, 23:13  #24 
Oct 2006
vomit_frame_pointer
2^{3}×3^{2}×5 Posts 
That's a pair of monster factors. Impressive!
Last fiddled with by FactorEyes on 20080718 at 23:14 
20080718, 23:47  #25 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·113 Posts 
Thank you. (I did all ecm up to the t50, but then  one can never be prepared for such a great split.)
My thanks go to Jasonp for the msieve (need I say more!) and to Greg for the fantastically effective sievers. This could have been a month job, but with Greg's sievers I was able to squeeze it into the 2,5day weekend on 8cpu's ...and then a 3,5day Lanczos. This is of course within the framework of Makoto Kamada's Factorizations of nearrepdigit numbers You're right, the c200's are no longer what they used to be. Sergey 
20080807, 06:02  #26 
"Frank <^>"
Dec 2004
CDP Janesville
2·1,061 Posts 
Continuing in the spirit of this thread, here's a factorization that came up in my factoring. I'm doing work on aliquot sequences and while factoring a number in the sequence starting from 483570 I ran into a c109 that had a very nice split:
Code:
N=3916544839567831037197929061130658865990153512796321700002919410571148541456293739142265233087865070538878483 ( 109 digits) Divisors found: r1=1195853321473814365126729514302766586119987697269752141 (pp55) r2=3275104704932319522075280744447318143325990375356349663 (pp55) 
20080821, 19:02  #27 
Mar 2007
Austria
2·151 Posts 
Lucky punch?
Question: is a p51 by ECM after about 560 curves at B1=11M lucky?
Code:
GMPECM 6.2.1 [powered by GMP 4.2.2] [ECM] Input number is 10594028369831114716682888330845541566105401124620505895213725128397891350870967330967394277735211887867089454105665163 (119 digits) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=861666340 Step 1 took 46698ms Step 2 took 25614ms ********** Factor found in step 2: 495436223298434385356722609135189152207142936793249 Found probable prime factor of 51 digits: 495436223298434385356722609135189152207142936793249 Probable prime cofactor 21383233343940664218943433891745463379743409952464040968535330972587 has 68 digits 
20080822, 08:08  #28  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·7^{3}·17 Posts 
Quote:
Paul 

20080822, 10:28  #29 
Mar 2007
Austria
456_{8} Posts 
The integer is the cofactor of (4ยท10^163+17)/3. I think snfs would have taken a bit longer on my machine.
nugget. Last fiddled with by nuggetprime on 20080822 at 10:53 
20080822, 20:08  #30  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10057_{10} Posts 
Quote:
But that's just my 2 cents, I may be wrong. S 

20080822, 20:22  #31 
Mar 2007
Austria
2×151 Posts 
@Batalov: I maybe forgot to mention that I've used a quadcore machine(Q6600) with all for cores ECMing. So it took just about 11/4=~3hrs. Anyway, I didn't know of the 2/7 rule and Snfs/Gnfs might have been more efficient(using all cores,optimized 64bit siever).

20080822, 21:37  #32 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
178F_{16} Posts 
i think the 2/7 rule applies to optimal cpu selection
as far as i am aware intels are worse than amds for nfs but amds are worse for llr than intels i dont know if there is anything like that with ecm 
20080824, 00:37  #33 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·113 Posts 
I am well known as a politically incorrect person im my circles. (hopefully not here ...yet).
But the following might offend some people, as well as also sound bitter (towards any recordholders), which it isn't. When I am listening to other people, I hear when the are helping me by criticizing me. Even if it is insulting in form. That's one lesson I think I was happy to acquire from life  people are helping me by criticizing me or my work. They are not helping me by keeping silence (or laughing behind my back). So here goes. Some of the ECM and/or QS records are in existence only because they were the wrong method to use. In 2008, if one spends six months for a QS on a 120digit number, yeah, that's a record size for QS in some communities. But it's a wrong method! They could have been done with the number in 2 days with GNFS. Same here. If one doesn't get past these 2/7 (of digit size or for GNFS), 2/9 (of SNFS complexity for SNFS) rules early enough in their learning process, they may well get amazing fits of ECM luck but will the get to snfs230 or gnfs156 or whatever... No, their computers will be loaded with tons of ECM for years... It is a lottery as opposed to a deterministic, if boring (and seemingly long) process. Listen, I am guilty of the same! ...don't reach for your revolver. I got into P.Z.'s top 50 ECM table by luck leaving the ECM on a 143digit number overnight with B1=110m and got a 56digit factor on a 82nd curve or something like that... I had no intention (and or resources) to finish a 110m ECM run  I simply got lucky. Did it for just one night before doing GNFS143, which I was not ready for back then. Looking back, was there any sense in running B1=110m curves on a 143digit number? Nope. Could have never finished. Just got lucky. This is also the only XYYXF number in the ECM record tables, unless it is gone (it was 48th at arrival). Most importantly, I learned absolutely nothing by finding that factor, while by doing a competent GNFS I could have gotten ready to bigger jobs back then. Ok, just look for good ideas in what I just wrote, not for hidden insults. There are none! (At least none intended.) Peace! Serge 
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