Hi Everyone, I am working on my video on explaining this geometric proof about prime numbers.
I hope to be done soon, I am really terrible at making videos. My greatest skill is just being a friend and listening to people, so working on this alone at home is kinda killing me. Hopefully I will be done soon.
I wanted to give you an update though! For anyone who cares. I am getting through it, and doing my best to make it clear as possible, because this proof is about much more than twin primes.
It is a proof that primes represent a geometric logical state.
The Twin Prime Conjecture is merely a consequence of this same logical state.
In fact, I wrote this quick update post for all of you here in 3blue1brown who care to follow, because I think I can prove Twin Prime Infinitude easily here now, now in just a few sentences.
Consider Counting in my program: The only requirement for a twin prime center is this:
clock 2 : ZERO
clock 3 : ZERO
clock 5 : anything except ±1
clock 7 : anything except ±1
clock 11: anything except ±1
clock 13: anything except ±1
...
With one exception being when each prime originally opens.
If you are counting using the modular cycles I have shown in my other 3blue1brown posts, then these are the only conditions required for a twin prime center.
You cannot look at the CRT configurations alone and arrive at the correct numbers, because the CRT method by itself loses information.
But when you are strictly counting forwards, you always know your position.
This allows you to always keep track of the valid configurations.
It is obvious to see then, whenever we add a new cycle, CRT demands and says that we will gain that many new valid configurations....
But viewed geometrically, we can think of squaring each prime as raising it up a dimension--- such operations looks like this:
When I am calculating Phase Address tables for the modular cycles, or clocks, and factoring them together, that is what I am doing. I am completing the square for that particular primes phase addresses.
When I complete the square, it naturally gives me an axis.
When I fold along that axis, I get the twin prime locations.
You can see it clearly in how simply it works in this python file
When I choose to view the clocks positions at mod 2 0 mod 3 0 and all other clocks away from their own boundary, I am specifically choosing twin prime locations.
If I were to instead only consider when mod 2 and mod 3 and mod 5 are all at zero, then I would be looking for primes separated by 30.
To me, this is already solid proof of the twin prime conjecture, so I am not sure where the disconnect I am having with people truly is, but hopefully once I have finished the video things will be more clear.
Consider this known geometric series:
1 + (2/n)^2 + (2/n)^4 + (2/n)^6 + ...
For n > 2, this geometric series sums to:
n^2 / (n^2 - 4)
But what if we also started a new geometric series beginning with each member, when n = 2?
So that you have essentially an infinite series of infinite series.
That is essentially what I am doing with my python function.
Anyways, I am slowly plodding along with my video but I really suck at it, haha. Thank you for your interest though!
