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20191127, 16:48  #12  
Nov 2003
1D24_{16} Posts 
Quote:
deliberately constructed the composite in such a manner. 

20191129, 00:32  #13  
Apr 2019
2^{5} Posts 
Quote:
Quote:
http://www.enseignement.polytechniqu...ts/Weger02.pdf https://blog.trailofbits.com/2019/07/08/fuckrsa/ https://www.researchgate.net/publica...ring_Algorithm ... ... ... BTW. It is so happened that you can come to R.D. Silverman from the inside of the first link  where the talk is right about Fermat. P.S. Since I'm not the author of the information in the links, I can not answer for them. 

20191129, 14:35  #14  
Feb 2017
Nowhere
5766_{10} Posts 
Quote:
Quote:


20191129, 14:49  #15  
Nov 2003
1110100100100_{2} Posts 
Quote:


20191129, 16:52  #16 
Feb 2017
Nowhere
2×3×31^{2} Posts 
I assume you mean ECM and SIQS are faster for tiny inputs or inputs with small factors. That leaves people doing stupid things.
For the numerical example that danaj gave (222 decimal digits), quoted above, even on my sluggish system the PariGP userdefined function Code:
OLF(x)={i=1;while(i<x,if(issquare(ceil(sqrt(i*x))^2%x),return(gcd(x,floor(ceil(sqrt(i*x))sqrt((ceil(sqrt(i*x))^2)%x)))));i++)} Code:
192606732705880508138303165129171270891951231683030125996296974238495711578947569589234612013165893468683239489 (If realprecision isn't high enough for OLF() to work, PariGP will issue an error message. Adjust as necessary.) 
20191129, 19:29  #17  
Nov 2003
7460_{10} Posts 
Quote:
If such a number has been constructed we don't need improvements to the algorithm. 

20191130, 04:24  #18 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{4}×13×31 Posts 

20191130, 14:23  #19  
Feb 2017
Nowhere
2×3×31^{2} Posts 
Quote:
(1) the number was constructed by another person who thought it would be hard to factor, and (2) danaj was merely arguing that one shouldn't dismiss having the method from one's toolkit. And that's all I'm saying. No argument that Fermat's method is useless as a general factoring method. No argument about improving a useless method being a waste of time. Just out of curiosity, though: What general method would factor the example C222 in a reasonable length of time? 

20191130, 14:41  #20  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{4}×13×31 Posts 
Quote:
M: Hey look, we improved method A with device X. Yay us, we are the greatest. N: Yeah, okay. But method A is pointless and useless, so you are wasting your time. Methods B, C and D already outperform A. M: Oh, yeah, you are correct. ... But, wow look, device X can also be applied to method C. N: OMG, that is so cool. No one else saw that previously. You guys are the greatest. Ya never know. It could happen. 

20191130, 15:07  #21 
"Rashid Naimi"
Oct 2015
Remote to Here/There
4302_{8} Posts 
Which one would track better in snow?
A round or square wheel? Which one would be an improvement over squarewheels for an onsnowdriven vehicle? Round or triangular wheels? For the literally detailed version, let's assume that the vehicle is equipped with adjustableelevationmaintenance skis on the side, to avoid digging in the snow. Last fiddled with by a1call on 20191130 at 15:34 
20191201, 03:59  #22  
Aug 2006
3×1,993 Posts 
Quote:


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