Prime distribution, twin primes, and Riemann

[Spacemoss]

Merged into one thread.

Hello, I am looking for feedback, conversation, and peer review on some related functions I have. If these are your field or are of interest, leave a reply. There is:

A function for the number of factors of a number.
A function for the specific factors of a number.
A function for the Exact Prime Distribution.
A formula for the n-th prime number.

Using Waves to Determine Primes.pdf

(717.18 KiB) Downloaded 46 times

I included the pdf on xkcd and a photo album of the pdf with some added formulae panels at the end can be found here: https://www.facebook.com/media/set/?set=a.413113782389844.1073741829.100010736770647&type=1&l=a69f58f077

The added formulae panels have many interesting relations on them, and relate to he ongoing questions portion of the pdf. I may post panels here as pictures if needed.

[Spacemoss]

The attached paper claims to prove the Twin Primes Conjecture using the following technique:

It defines a surface set containing all of the composites and no primes.
It defines a 2nd surface for the values 2 away.
It shows a map between the elements NOT on the 1st surface (the primes) and the elements NOT on a related 3rd surface.
It shows a map between the elements NOT on the 2nd surface ( the 2-aways) and the elements NOT on a 4th surface.
It shows that an infinite number of elements can always be found that are NOT on either the 3rd or 4th surface.
It shows that those found elements correspond to either just a regular prime, a Twin Prime, or an odd composite.
It shows that if you remove all the non twin primes, and odd composites, that there are still an infinite number of Twin Prime generating elements in the set remaining.
Therefore it can always generate another Twin Prime pair.

Twinproof Update.pdf

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It can also be found here as a photo album:

https://www.facebook.com/media/set/?set=a.413119242389298.1073741830.100010736770647&type=1&l=25fc972aea

This paper is not 100% formalized, and the more technical reader will wish to begin with section 2. The 1st section labeled update, is only a loosely written list of the logic in more formulaic statements and is not as easily followed or full explained. If you find this interesting, leave a comment, thanks for looking.

[Spacemoss]

Hello, this is the least refined of some material I am working. It suggests that you can use an Inverse Fourier Transform to Create a Bijection between the summation of the Dirichlet eta equivalence of the Riemann Hypothesis and the continuous wave function. The wave function then shows that the real part of the complex input can only take the value of 1/2 due to the functional symmetry of the odd and even and real and complex parts of the summation.

This work is mostly in formula panel form at this point and currently lacks a full write up.

The panels can be found as a photo album here:
https://www.facebook.com/media/set/?set=a.413122689055620.1073741831.100010736770647&type=1&l=f6d2ca1aab

If this is interesting to you, leave a reply, thanks for looking.

[gmalivuk]

I merged these into one thread. You don't need to start three separate threads about such closely related topics.

[Spacemoss]

Thanks, I actually was going to do all these 3 as one, but I also wasn't sure if it would be too much on one thread. This is perfect.