20050308, 14:14  #1 
Feb 2003
2^{5} Posts 
Is this a feasible factoring method?
Let N be a number that is proven to be composite but whose factors are unknown. Let F be a number less than the square root of N.
Then N = b mod F. Increase F by 1, and b decreases by a certain amount. Further increase of F causes further decrease of b until b reaches a relative minimum and jumps back to a large value. If the relative minimum of b is zero, then we have a factor. But if this procedure is applied to large numbers, it would take quite a while before we arrive at a relative minimum of zero. My first question is: Is it possible to determine the relative minimum value for a particular F? I.e., If N = b mod F = c mod F+1, where N,F,b,c are known, can the relative minimum be identified from those values alone? My second question is: Is there a derivative for N = y mod x? If there is, can equating y' to zero identify ALL the minimum values? 
20050308, 14:26  #2  
Nov 2003
2^{2}×5×373 Posts 
Quote:
some mathematics? It is clear that you are ignorant of even the basics. To start with your first (erroneous) claim. (1) Let N = (10^1131)/9. Let F = 17 Then N mod F is 1. Increase F by 1. Explain how b decreases... And your statement 'b decreases by a certain amount' is hand waving nonsense. Beyond the simple fact that the statement is fault, the phrase 'by a certain amount' is so totally lacking in precision as to be meaningless. Didn't you even bother to try some tiny examples before posting this nonsense???? It is gibberish. As is the talk about a 'relative minimum' Your question about derivatives shows that you do not understand what a derivative is. Why then are you even discussing them? Before one begins a discussion of this type it is imperative that you do some basic background reading and at least partially CHECK YOUR CLAIMS. You have done none of this. You are a troll. Go away. 

20050308, 21:33  #3 
6809 > 6502
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Aug 2003
101×103 Posts
10,103 Posts 
Bob comes off a little strong, but he is correct in suggesting that you try your method out quite a bit, before you suggest that it may work.
Studying up is good. (Bob is a true expert.) Here is a graph of an example of why your idea won't work. I took a number 1373 (prime) and used mod and graphed the results. Across the bottom is the divisor and up the side is the remainder. See how it is saw toothed? Even if the number had a factor, a similar pattern would be seen. mod values tend to swing around alot. Last fiddled with by Uncwilly on 20050308 at 21:36 
20050309, 07:16  #4 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Mr. Silverman,
I suggest that you apply the same standards to yourself in regard to areas outside your peak competence that you apply to others. You obviously are as ignorant of some basics of human communication as you judge others to be of mathematical basics. Before you slam someone with "It is clear that you are ignorant of even the basics", please stop to consider how far such a retort will take you outside your sphere of competence. In this case, it is not at all clear that "1260" is ignorant of basics  someone who is genuinely as ignorant as you imply would not have been able to compose such a readable posting as "1260" did. Couldn't you figure that out? You clearly lack the training and/or ability to appropriately match the intensity of your criticism to the context in which it is applied. Please keep that in mind, and reduce the emotional content of your responses so that you do not demonstrate your own incompetencies so vividly. We respect your obvious mathematical abilities and prowess. You don't need to put down others in order to demonstrate your greatness in math. But your overthetop slams can earn you disdain from those who have genuine ability in communication and tact. 
20050309, 07:40  #5 
10010110_{2} Posts 
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20050309, 09:14  #6 
Aug 2002
Termonfeckin, IE
ACC_{16} Posts 
1260, I hope Bob's response doesn't make you feel too unwelcome. While others on this forum may not have the same level of mathematical training, they are not as harsh or as judgemental

20050309, 11:39  #7  
Nov 2003
2^{2}·5·373 Posts 
Quote:
(2) The original poster did not ask questions; instead he/she made some rather bold pronouncements. It was `totally clear that he/she did not spend even 30 seconds checking these pronouncements because a trivial check would have revealed that they were wrong. (3) One thing I do not have in abundance is time. When someone asks about a 'method' it is their OBLIGATION to have at least done some preliminary checking. To do otherwise is rude to others who read the post. (4) When someone talks about a 'derivative' for a function defined only on the integers it IS clear that this person does not have even the minimal background to try to discuss this material. (5) I am hardly 'great' in math. But before I make some posting in a topic about which I know little (let's say Galois Cohomology for example), I take the time to read and study. To do otherwise shows discourtesy to the people I would be asking for help. PEOPLE HAVE AN OBLIGATION TO DO AT LEAST SOME PREPARATION BEFORE WASTING THE TIME OF OTHERS. If the people in this forum want help, it is imperative that they first DO THEIR HOMEWORK. There is nothing more aggravating to a teacher than someone who asks for help without having done their homework. It is too bad that you don't understand this obligation. 

20050309, 14:36  #8  
6809 > 6502
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Aug 2003
101×103 Posts
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20050309, 14:47  #9  
Feb 2003
2^{5} Posts 
Quote:
However, when b = 1, there is still a possibility of b decreasing if F+1 was a factor of N. However, if it was not a factor, it would shoot up to a relative maximum. Last fiddled with by 1260 on 20050309 at 14:54 

20050309, 14:53  #10  
Feb 2003
40_{8} Posts 
Quote:
It's okay. I've received stronger words than those. I guess that's part of learning. Don't be afraid to be called a troll (especially if you're one ). Yes, that's what I was after the lower ends of the swings. Isn't there a faster way to determine them without checking all values? Last fiddled with by 1260 on 20050309 at 14:58 

20050309, 15:03  #11  
Feb 2003
2^{5} Posts 
Quote:


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