Primenumber and dividers (complex chance distribution)

Dec 2014
52
12
Netherlands
Hello,

Last couple of weeks I did some intensive puzzling (but it started 10 years ago). Finally I came up with formulation of primenumbers and other divisors.

With help of: "complex chance distributions."

I am not aware of any of the status regarding prime research. So it might be old news. But shore is new news to me!

It would be honoring if my findings where reviewed and discussed. That many questions and findings came up and I am not able to answer them myself,

I am new to (this) forum and not very comfortable communication over a forum.

Please find both a report and presentation below. Hopefully the link will work.

https://drive.google.com/folderview?id=0B1BBIFPrdzYwWXowRXdGaVdsV1U&usp=sharing

Regards,

Vincent
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
Your definition of N(x) is circular: it relies on L, which in turn relies on N(x).
 
Dec 2014
52
12
Netherlands
Hello,

N(X) has surely strange behavior. But is there something fundamentally wrong?

Regards,

VInce
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
But is there something fundamentally wrong?
Yes -- you never actually define it! I could determine its definition if you gave the definition of L, but you don't define L except by inverting the definition of N(x).
 
Dec 2014
52
12
Netherlands
mmm, indeed my professional math is not correct.

Maybe I can try and explain:

Goal:
Create even and independent pulse widths for the cos(pi x/X)^N function for every frequency of capital X.

The reason: every frequency of X may not interfere with one other. Else we cannot determine the number of divisors for a number x.


The pulse width is defined as delta(x) from the maximum of the pulse. L is the limit value on deltax.


Thank you for taking your time,

Vince
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
That still doesn't tell me what L or N(x) are. I couldn't, for example, find N(91).

I understand the idea of using periodic functions to trace out the (prime) divisors of a number. I don't know how to make that computationally useful, though, since (1) you'd need to do this for a lot of divisors and (2) you'd need to compute these functions to very high precision, and both of these are expensive.
 
Dec 2014
52
12
Netherlands
Again thank you for your reply. And your time

If it is useful I do not know. Probably not then.

But during the discovery's. I was fascinated by the mathematics. For the first time in many years I had the idea I was doing something useful.

Coming from:
cos^N => to a chance vector in the complex plane. wow (for me then)

The contradictions fascinated me. The imaginary component totally lost when examining the problem in a different way. This result that the phi component (img) should/could be zero also resulted in a more simplified model. That in turn also seems to generate solutions.

The phi component and the chance function both could be calculated as function of an continuous k value. That simplifies the chance function (not the discrete N over k). And solutions are found.

But care was needed. When calculating the Re and the Img component they should be interpreted with and discontinuous k.

Just these small discovery fascinated me and I would like to learn more.

But my motivation actually diminished. Maybe that in time to come I like to investigate a little further.

Thank you for your interest,

Vince
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
It's a fascinating subject, no doubt.

I encourage you to study further. Just because something isn't (or doesn't seem to be) computationally useful doesn't mean it's not worthwhile. Take Wilson's theorem for example: despite some attempts, it's really not useful for computation, but it's beautiful and has been used to prove theorems.