20131006, 17:37  #12 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·41·71 Posts 
#8 is the type of response that is appreciated here. #7 was harsh but shares the feelings of many on this forum.

20131006, 18:56  #13  
Apr 2012
2·47 Posts 
Quote:
That was something similar I thought before doing that graphics. I created this graphs with Mathematica but I could try to do it with other software if you want. Code:
NN = 272123 tt = Table[Mod[NN, kk], {kk, 1, 1100}]; ListPlot[tt, Filling > Top, GridLines > {{503}, {}}] And the "useful" graphic Code:
NN = 272123; tt = Table[Mod[NN, kk], {kk, 1, 1200, 1}]; ListPlot[ Differences[tt, 2], GridLines > {{503, 541}, {}}] This is an example with small numbers and trying all divisors just to show you the pattern. My idea is, for big numbers, NOT to try all possible divisors but only a very small part of them, just enough to "draw" the curves. And then try to detect "hot" areas. And that's the question, of course I don't know if this could be useful. Maybe not just as a new method but in combination with other methods. I'm just an amateur on "number theory" and factorization methods, and as I said English is not one of my native languages. Regards Last fiddled with by skan on 20131006 at 18:57 

20131006, 19:21  #14  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}·3·883 Posts 
Quote:
Quote:
To the best of us, and to the worst of us, and to everyone in between. You have my sympathy and my assurance that you are in good company. Quote:
(For the benefit of other forum readers: Bob and I have been discussing these matters for many years, sometime by private email, sometimes in public fora and newsgroups, and once over beer in Cambridge. "These matters" include both intellectual concerns and our respective states of health) 

20131006, 19:48  #15 
Apr 2012
2·47 Posts 
Hello
I wouldn't like that this thread was closed. It would be nice if some administrator could "clean" some of the posts. And if somebody is not interested just look somewhere else. 
20131006, 23:09  #16  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010001110101_{2} Posts 
Hey, skan, from the title of your thread I gather that you yourself expected some criticism. You reiterated it now: you don't want the thread closed, you want to hear more. But there's a contradiction: at the same time, you want the thread "cleaned"? Of what parts? They are all more or less connected. Most of them have advice (some of which you may not like, but sound nevertheless).
On the bright side, you haven't received any really insightful answers yet, like Quote:


20131007, 10:39  #17  
Apr 2012
1011110_{2} Posts 
Quote:
Hello I meant "clean the thread from personal attacks and disqualifications", just like if nothing bad had happened. And leave all comments related with graphics, ideas, maths, science, computers... Regards Cheesehead, thank you for your support. Last fiddled with by skan on 20131007 at 10:40 

20131007, 15:29  #18 
Apr 2012
94_{10} Posts 
Hi Silverman.
I know there already exist many factorization and sieve methods. This is not intended to replace them, just to further restrict the sieve. I know the meaning of "Trial Division", and I even read about "quadratic sieve" and "number field sieve" some years ago. I'm not mathematician, just an engineer than loves maths. I do know what's "O(N^1/4)". I don't like "number theory" books because they are too theoretical for me. That's why I tried to focus it from a different point of view. Yes, There are relationship between N mod k and N mod (k+1). I can't explain them algebraically, but I guess you mean they are the patterns in the graphics. OK, just tell me it's evident this is not useful. Maybe somebody else could enjoy the graphics or get new ideas from them. 
20131007, 16:17  #19 
Apr 2012
5E_{16} Posts 
But I'm not trying to discuss about deep number number theory concepts but about heuristics and feelings.
Do you know Monte Carlo algorithms? Sometimes they can be used to solve numerically difficult integrals quickly, even if you don't know how to solve the integral exactly. This is just another way of doing things. Last fiddled with by skan on 20131007 at 16:22 
20131007, 16:27  #20 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2475_{16} Posts 
There already is a Monte Carlo factorization method. Since 1975.

20131007, 18:07  #21 
May 2013
East. Always East.
11010111111_{2} Posts 
To Skan:
It is no surprise to me that you are an Engineer. A lot of engineering is about observation. It's about observing a pattern and applying whatever knowledge is readily available to try to extend the pattern into something useful. That's exactly what you are trying to do here. On the other hand, you are debating with a mathematician. I've dealt with a few in my first couple of years of school and I think it's adorable how much they hate us. It's hard to blame them, really. An engineer like me takes four calculus courses (so far I have found no reason why you couldn't cut away 60% of the material and make two slightly more bearable courses rather than the four nightmares we did have) and has enough knowledge to work in several different fields. For example, I use "maths" in fluid dynamics, solid mechanics, heat transfer, thermodynamics and controls systems. Basically, the engineer works probably 5% as hard on any given subject and gets an answer with 15% accuracy. A mathematician would pull out his teeth trying to come up with a heat transfer equation for the most basic of systems but the engineer can take the most complicated ones, just do a bunch of tests, plots the results and write up a correlation for a curve that best matches all the points. Mathematicians hate that kind of thing but, much to their chagrin, that's the sort of thing that makes real application continue to march forward. Last fiddled with by TheMawn on 20131007 at 18:10 
20131007, 19:49  #22 
May 2013
East. Always East.
3277_{8} Posts 
I was simply making the distinction between the straightup "Math" and the "Engineering" where in engineering we can, usually, form a correlation to get "close enough" based on enough empirical evidence. To be perfectly honest, it wasn't meant to be criticism to either side. (Granted I might have been biased against mathematicians, but that wasn't the point)
I can't pretend to understand very much about what is being discussed. I saw some graphs and somepointswhichcouldclearlybeconnectedbyarelativelysimplecurvebutdonotofthemselvesconstituteacurve and at a glance there is obviously a pattern. I didn't really care much about the content because I again don't understand it. What got me was the question of could we begin this curve by learning a bit about a new number and then extend the curve and work closer to whatever values these might be. My first comment in this thread was seconding Cheesehead with respect to you being rude. Yes, you gave criticism as is your right but it just came out a bit harsh. My second comment was regarding the Engineering vs Mathematics or Approximations vs Exact Solutions. Of course, now that I look at the graphs themselves I feel myself gravitating a bit more to the "not entirely useful" side of the fence. The "curves" in the third graph are actually just tending toward y = x, y = x, and y = 0 which unfortunately do not tell us anything. Pretty? Sure. Useful, not so much, I'm afraid. Last fiddled with by TheMawn on 20131007 at 19:49 
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