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Author Topic: factorisation of semi primes using ray  (Read 5961 times)
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zander
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on: May 06, 2010, 12:18:07 am » posted from:Worcester,Worcestershire,United Kingdom

Dear Sir/ Madame,
Is there a way of using a ray in a machine to determine the factors of a number ? For example, can a machine be calibrated to '87' and then some how reveal '29' and '3' as the factors.

Also, is there machine design that would be able to factorise very large numbers without having to rely on an impossibly accurate design. For example, a machine may be able to 'zoom' in on the factor by re-calibrating the machine over an increasingly small amount but over the same physical area, thereby not relying on the measurment of an extremely small angle/space.

Thank you for your time ! Smiley
Cheers
Zander
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Fu-Kwun Hwang
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Reply #1 on: May 06, 2010, 10:03:09 am » posted from:Taipei,T'ai-pei,Taiwan

The first part can be done with computer program easily. (A while loop will do the trick)
e.g.
Code:
Assume N is the input number, P is a possible factor of N, PN is the number of count;

PN=0;
P=2;
while(P if(N%P==0){
  N=N/P;
  PN=PN+1;
 }else{
  echo "*P^PN";
  PN=0;
  P=P+1;
 }

}
However, I do not fully understand what you mean in the second part of your question.
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zander
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Reply #2 on: May 06, 2010, 05:12:50 pm » posted from:Worcester,Worcestershire,United Kingdom

Hello,
Thankyou for your reply.

I am interested with using a ray because the method would be analogue and could therefore check every possible factor in the same short amount of time, regardless of the size of the semi prime. Whereas the computer program's speed at determining the correct factor decreases as the amount of possible factors increases.

The bad part of using an anaologue ray method is that as the number to be factorised increases, so would the accuracy of the machine. In the second part of my previous question, I am asking if there is a machine that uses an analogue method and also does not have the problems of being limited by accuracy.

I am not aware of any other ray factorisation device ? I have created a method of using a ray. Please see the attachments. This machine uses these 2 facts:
1) that if you square the number being tested and add the squareroot of the modulus against the semi prime (87), a multiple of the modulus is revealed
109^2 = 11881  mod(11881, 87)= 49  mod(109+49^0.5,87)=58

2) that if you square a multiple of a factor and then calculate the modulus, the answer is always another multiple of a factor. 
Example of how multiple of factor repeats :  58 = 2 x 29  58^2=3364  mod(3364,87)=58
Example of how non factor doesn't repeat :  57  57^2=3249  mod(3249,87)= 30

Other non factors, on the other hand become 'noise'. Over sufficient interations, this factor pattern becomes measurable above the noise. My machine could also be re-calibrated over smaller intervals, where an irregularity in the noise occurs. This allows 'zoom' ,  thereby removing the limitation of the maximum accuracy of the machine. The only limitation is the amount of reflections a ray could have until it losses all of it's energy !

I can send you a spreadsheet that demonstrates this for any semi prime, and shows the angles at all stages, if require.
Thanks again for your time.
Zander Hack


* factor found.png (34.76 KB, 1575x811 - viewed 266 times.)

* lower clibration BOX1-3.PNG (26.43 KB, 776x607 - viewed 220 times.)

* upper clibration BOX1-3.PNG (28.66 KB, 793x677 - viewed 261 times.)
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zander
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Reply #3 on: May 11, 2010, 03:16:30 am » posted from:Tewkesbury,Gloucestershire,United Kingdom

Hello Professor,
I have attached a spreadsheet that demonstrates how the factorisation works in the previous diagrams, for any semi prime. I have also added a list of primes on the 2nd worksheet so that you may pick and enter any 2 primes into cells a3 and b3. The diagrams I attached before are equivalent to row 19 on this spreadsheet (which is already set to 87). You might have to wait a few minutes for all the values to change, after changing a factor, depending on the speed of your computer. I have added a macro button that reduces the amount of cells for semi primes to speed things up for the user investigating smaller semi primes.

Because this is a digital simulation of how the analogue equivalent works, the result becomes hit or miss with semi primes over 30000. You would have to increase the amount of rows even further to accommodate larger semi primes.

Could this be simulated with a ray and would it work ? I'm not familiar with the limitations of lenses and whether they can be applied to this solution ? I can not relate the angle going out of Box1 to the angle going into Box 2 because they relate to the equation for Tan.  The length of the 'opposite' is squared but the angle isn't. Huh I think the graduation on the initial calibration would have to be non-linear.
Thanks again


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zander
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Reply #4 on: May 11, 2010, 05:03:22 pm » posted from:Tewkesbury,Gloucestershire,United Kingdom

corrected some bugs !


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Reply #5 on: May 11, 2010, 09:00:50 pm » posted from:Taipei,T\'ai-pei,Taiwan

I am really busy recently. I will try to look at your code when I find free time to do it.
Sorry!
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Reply #6 on: May 24, 2010, 09:00:47 am » posted from:Taipei,T\'ai-pei,Taiwan

I am interested with using a ray because the method would be analogue and could therefore check every possible factor in the same short amount of time, regardless of the size of the semi prime. Whereas the computer program's speed at determining the correct factor decreases as the amount of possible factors increases.

The bad part of using an anaologue ray method is that as the number to be factorised increases, so would the accuracy of the machine. In the second part of my previous question, I am asking if there is a machine that uses an analogue method and also does not have the problems of being limited by accuracy.

Do you know RLC circuit can be used to solve any second order differential equation?
The computer was first designed as an analog device. However, precission is the main reason why computer was switched to digital device.
For example: two digits meter can be very cheap. However, 3 digits meter might cost 10 times.
4 digits meter cost even more. And it is very difficult to operate meters with more than 6 digits (need to be in constant temperature environment).

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zander
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Reply #7 on: May 28, 2010, 06:50:34 pm » posted from:Gateshead,Gateshead,United Kingdom

Thank you for your reply. I was not aware of this RLC device and the limitation for it appear to be very similar. With regard to it's application to solving second order equations , this is too complicated for me a present ! But, I will try and understand the background and maths to this method. This is very intersting further reading for me.

Presumably, if this accuracy limitation did not exist, there would be many existing ways to perform this factorisation already. Would you be able to comment on whether my theoretical proposed ray method would be able to perform factorisation if the accuracy limitation did not exist ?

Thanks again, Zander
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Reply #8 on: May 28, 2010, 10:30:11 pm » posted from:Taipei,T\'ai-pei,Taiwan

There are alway more than one way to do the job.
Some way are more efficient, some way are more elegant, some way are more interesting, some way are more fun, ...

It is alway fun to think of more than one way to do things if you have spare time or just do it for fun.

I would recommend you do what interest you most and we alway can learn something from what we did.
Keep up your work!
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