20181224, 18:22  #1 
Dec 2018
2_{10} Posts 
Diamond multiplication and factorization method
I've found these two patent papers:
https://patents.google.com/patent/US20120066282A1/en https://patents.google.com/patent/US20140207839A1/en The authors claim that they have found a polynomial method of factorizing integer numbers. I've read it carefully and the interesting thing is that the method of multiplication from the first one really works for any two odd numbers. I've even implemented it in C# and it seems correct. I have never seen such a method before and it seems that every composite number has this diamond structure guided by "whole zeros". For two numbers of different bit size I just always put the smallest one on the left leaning side and prepend with zeros. It works also for even numbers after removing trailing zeros from each number to make them odd, perform the operation, and then sum and add the removed zeroes to the product The factorization however is not described really well here. I understand finding the complementary structure and I can see how it may work for small numbers  even on a piece of paper, but it seems when you try to project it back to twodimensional diamond form it still involves some trial and error process that grows quickly in size, unless I don't understand it fully. The second paper is some messed up 3D stuff, but It is almost the same method. I don't know if this is something important, but I wanted to share just in case it is and I just don't understand it fully. 
20181224, 18:46  #2 
Aug 2006
1011101100001_{2} Posts 
It just seems so unlikely to work, and the payoff is so small (because even if it turns out to be true, the method is patented), I can't be bothered to even look it over. All the more so since you looked at it and found it inscrutable.

20181224, 19:51  #3  
Feb 2017
Nowhere
10645_{8} Posts 
Quote:
Quote:


20181224, 20:23  #4  
Dec 2018
2 Posts 
Quote:
1. It seems that multiplication method and the "diamond form" of every composite number is real thing. 2. The factorization method (poorly described) also work  you can "convert" from 1D binary form to 2D diamond form knowing N and it's N0 complement. but I'm not sure if and how it is faster than just trying every combination. Quote:
Quote:
Last fiddled with by datblubat on 20181224 at 20:37 

20181224, 21:56  #5 
Aug 2006
3^{2}×5×7×19 Posts 

20181224, 22:59  #6  
"Curtis"
Feb 2005
Riverside, CA
2×3^{2}×5×53 Posts 
Quote:


20181225, 17:29  #7 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
908_{10} Posts 
Regardless of the merits or lack thereof in these patents, there are a lot of reasons why the patents would be abandoned. Sometimes it is purely monetary to help budgets. Sometimes the point was merely to have it protected for a limited time, and now it still works as a defensive publication. It's much cheaper to publish for defensive reasons in one of the boutique journals meant for that purpose, but often the company is undecided and might choose patent to be safe, then changes their mind. The engineers are almost never involved in that discussion.
I don't think you can read too much into this. I laugh every time I see the articles like "International ApplePackardSoft filed a patent on bird collars for rural WiFi  how will this affect next year's products? An in depth look at how the company is signaling a fundamental shift in direction." Um, no. Some engineer got a bonus for writing up an idea. Someone in legal tech thought it was worth looking into. More discussions and they decided it wouldn't hurt to file a patent, for all sorts of different possible reasons. Slog through the writing and filing process and there you go  a patent that only 10 people in the company even know exists and no further work will ever be done on it. Every now and then these sorts of things strike gold, or it turns out that rather silly patent has just enough overlap to be worth tossing into a bin of "we'll trade you these for all of those" or a "you sue us, we'll countersue with 32,767 patents we claim you're infringing." It turns out it is worth spending $50k each on some iffy patents, plus $5k each on a bunch of defensive publications and trade secrets, on the off chance that one of them will prevent a lawsuit that costs the company hundreds of millions. Or, as I witnessed a few times, was enough incentive for someone to work a little in their spare time and flesh out some ideas, some of which went into products and arguably were worth millions of dollars. 
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