u/Defiant_Efficiency_2

{Post Update : I have now generalized this to be a forumla for showing all primes as perfect divisors of their simplex dimensional space.... get ready for Volume 4. Here is finished paper, making a new post about it now. }

Hello 3blue1brown math wizards! I am back with a new formula regarding primes and the Golden ratio! - Skip to the new paper

In my previous 3blue1brown posts here and here I proposed a solution for the Twin Prime conjecture. I attempted to prove the twin prime conjecture by reorganizing the primes into a pattern which I could find symmetries with the Golden Ratio Series.

However with the helpful feedback from a few redditors in this channel, I was able to see that my construction still required Prime and Prime squared domain certification, and could not give detailed enough information on prime or twin prime distribution.

I believe I have a solution for that problem now, and what I present to you now, I believe has never been discovered before.

What I have done in my current construction, is defined a formula that predicts the exact center of prime distribution in a given domain.

This formula does not require external prime certification, and arrives at the exact center which splits the primes into equal upper and lower domains, inside of a given square domain. If there is an even number of primes, it will find the exact center, if there is an odd number of primes, the center will itself be prime with equal terms above and below.

This formula therefor, does in fact give information about the distribution of primes.

I am not claiming this specific paper is itself a claim for Twin Prime Conjecture. Rather, this paper is a conjecture itself, that this specific formula can and always finds the exact center of the primes.

Further, I speculate that I will be able to now use this formula to further measure the distribution of primes, and if I put it back into my previous paper I believe I can find that it becomes the proof I was looking for.

Regardless, I offer this specific paper and formula for finding the center of primes, because in and of itself it is already valuable, I believe, for what it can teach us about prime distribution.

I leave it to further work from myself and other members of the community, to be able to take this current formula and make further deductions about prime and twin prime distributions.
But for my self I leave that work to tomorrow or another day as getting this paper to where it is has temporarily exhausted me.

I am grateful for anyone's feedback on this paper, and if you can help me find any flaws in it, I would be grateful, if in fact there are any.

I link the above video from 3blue1brown because It's kind of asking the same question I was asking... which is what if I can solve this problem regarding prime distribution by jumping up into higher dimensions.

I will leave the full description of how this system works for the paper itself.

But I will just generally say it here: I have found that by counting through The simplex dimensions, on a diagonal, and applying the transformations that requires. I am able to recursively generate the centers of primes in given arbitrary square domains. I do this by starting at the smallest numbers and counting up, following the rules given to me by the simplex dimensions and the golden ratio numbers and I arrive at a specific formula which appears to ALWAYS give the exact center of the primes in a given domain.

Here is the new paper, thank you for your time everyone.

Hello fellow 3blue1brown fans,
{Addressed the issues brought up in comments. here is the updated paper}

In my previous post I was given the feedback that I needed to fix my vocabulary to be standard maths. Additionally that I had spent too much time explaining things that weren't important.

I have fixed those problems now, I was able to remove 14 pages of over explaining, while retaining the core logic and adjusting the language for consistent clarity.

I am still claiming I believe this to be valid, and after 100k views on theydidthemath, their best objection was about the same as here, except you people are more kind lol.

That's why I call this my home for reddit, Grant has created such an inspiring place to foster learning for the sake of fun and curiosity, making theories and testing them.

And so I ask of you, can you help me test my Theorem? Because for me it passes all the tests required of it.

No one will take me seriously though until One person does.Since I am not a person of respected academic background, (Grade 10 education, but I've read lotsa books![not to be exemplified by lazyness to use proper punctuation.])

So I ask you as a friend, can you find a flaw in this logic or math? Because I can't.

Please upvote if you can't find a flaw so that perhaps someone who can find one will see it.

Thanks for your time people.
paper link

Hello, math wizards. I am an amateur researcher, and I think my twin-prime argument is ready for serious scrutiny. I would be grateful to anyone willing to read it, challenge the exact theorem chain, or potentially help me submit it to arXiv.

I also have a companion python program which utilizes the math stated in the paper.

The construction is fairly simple to summarize:

• Generate the Sieve of Eratosthenes recursively using additive crossover rows.

• Show that prime rows through P classify every integer through P².

• Extend the next block, from P² to 2P², using only the finite correction from P to √2P.

• Organize possible twin primes around centers 6m, with boundaries 6m−1 and 6m+1.

• Show that each new prime q closes two center classes and leaves q−2 open.

• Use the Gold boundary P² < φP² < 2P² to divide every expanding square domain into two exact widths whose ratio is φ.

The central claim is stronger than merely saying twin primes never disappear: the number of certified twin-prime pairs inside successive square-domain blocks increases without bound.

I have also included a companion Python program that generates its own recursive prime rows and finds twin primes through the 6m-center construction. It does not call an external primality-testing function, and it can be run to any finite boundary your RAM and CPU can handle.

I am looking for precise mathematical criticism. One flaw is enough to disprove it, please state the exact equation or logical deduction you believe it fails at.

Paper:

Companion program:

Shot out to anyone who actually understood this paper... please give me an upvote, because I guarantee the people who don't understand it will downvote!
<3

Hello fellow 3blue1brown nosers , I have been recently studying prime numbers, and I wondered if it is possible we can compress information about them?
I am wondering if it actually is possible to find repeating patterns in the prime numbers but only if you somehow compress the information in the numbers which came before it?

This post relates to 2 of my previous posts here on 3blue1brown on the same subject so I wanted to give anyone an update who was interested in the subject.

Over the past couple days I have been experimenting with creating a python function which could show how my idea for Twin Prime infinitude works. I came up with a recursive function that predicted exactly when the Twin Primes should show up. Image of function output

But I ran into an interesting problem, that came with an interesting solution that relates to compression and the 3blue1brown video I linked.
I found that I could come up with rules for when I should expect to see a Twin prime, and those rules worked.... except only for so long, and then they stopped working.
But then, I came up with an idea about reset points. Numbers like 4, 16, 256, and 65536, acted as perfect reset points to make an adjustment to my system, and then continue onwards for another few members of the series before requiring a second correction.

The most interesting part about this though, is that the corrections I was applying were not just random corrections. Those corrections came from a very specific source.... the Golden Ratio.

I found that if I put my reset points into the Golden Ratio series, and then multiplied them by the appropriate number according to their place in the GR series, that became the exact correction needed to reset my system, and continue to generate twin prime centers for a period of time.... before eventually requiring another correction from the Golden Ratio series and continuing onwards.

I created a python function which you can see on Github that shows what I did, but I was able to generate twin prime centers using this method, in series, up to 84 digits long!

I am currently working out the finite steps between k2 = 256^2 and K3 = (256^2)^2
However I have the major steps of K laid out all the way up to K13 I think.

If you understand this type of work please take a look at the python file, I would be really grateful to have some people help me to think about this problem.

I am also happy to answer any questions and give my understanding in my own words about what I am doing here.

I think it's pretty fun and interesting that Grant recently published a video about compression, and then my Work on twin primes ended up becoming about compression as well.

Edit2 {Updated paper revised section 6 and 7. Added certification for prime }

Edit{ I created a table with values to make the math more clear, see tabs for phi-prime bridge}

So assuming this twin prime proof is true, how does it relate to Collatz conjecture?

Imagine a number line, as a circle. Consider all the integers. Now Double the refinement of scale but make a second circle of the same size.
Now all prime numbers greater than 2 on the second circle are included ONLY in the odd numbers, by definition.

You could repeat this process infinitely many times and you just increase the refinement scale by the square.

However, as you do that, the prime numbers greater than 2 ALWAYS fall into the odd numbers compared to its previous circle.

This allows you separate 2 as the singular unique prime that remains prime at all levels of refinement.

I think this is how it reflects Collatz conjecture, because it basically says, if you exclude every other fraction through infinite operations, what remains is the square root of 2.
And to me that kind of makes sense because it represents a balance point.

A more full understanding of how it relates to Collatz could probably be reached through statistical analysis of the Twin Prime Conjecture in this paper, if it is validated.

Furthermore, I am not claiming this is a proof for Collatz, I am claiming that it is a proof for the Twin Prime Conjecture, so if you happen to see a proof for Collatz in this work, I implore you to make the connection yourself and publish your work, it would help to validate my own work, and I don't have interest to solve Collatz right now because I am still working on validating my Twin Prime Conjecture.

Since this is a channel for Collatz thats why I started off with the assumption of choosing this framework to be true... because then we can discuss "IF" it's true, does this also help to prove Collatz?

I recently finished a paper presenting a proposed proof of the twin prime conjecture.

Unlike the usual sieve-based approaches, the argument does not try to test increasingly large numbers or estimate how often prime pairs survive. Instead, it treats the branches 6n ± 1 as a recursively normalized structure and studies the completed “doorway” between finite composite partitions.

The main chain is:

6 → 1/5 → 5 → 1/4 → 4 → 1/3 : 2/3 → 1/√2 : 1 : √2

The reverse doorway operation,

x_(m+1) = 1 + 1/x_m,

generates Fibonacci ratios that remain rational at every finite stage but converge to the irrational fixed point φ.

The argument is that composite numbers belong to finite product partitions, while the completed irrational doorway remains outside every finite refinement. The reflected doorway preserves a gap of exactly 2 and repeats through infinitely many tiers.

Here is the full paper:

I am grateful for anyone who has the time to give this some serious thought. I am open to feedback on if I have made any definite errors of logic (besides choosing to be an unemployed mathematician)

Edit2 { I created a table with values see tabs for phi prime bridge }
Edit {Updated Paper: Significant rewrite for clarity and consistency. The most important result from this paper is that the gap which survives all refinements is phi.
Simple one sentence proof (derived through algebra in paper) " Start with the number line, scale it by 2, now rotate your line by phi, now none of your numbers are on the previous integer numberline while perfect squares of 2 always remain related between phi and root 2}

Hi everyone, I am claiming to have a Twin prime conjecture proof, algebraically, related To eulers reciprocal function and viewing partitions as a way to express primes as part of a partition series. You can skip to the end if you want to just read the paper, but I wanted to share my story of how I got to this point, because I wasn't even trying to solve the twin prime conjecture... I was working on something completely different and I discovered this almost by accident.

I was studying the hydrogen spectral lines and how they relate to the Balmer series. You can see some information about it in this 3blue1brown video

I was playing around with the Balmer series by imagining what if I inverted it and reflected it between the values of 1 and 2, and then I re-imagined the 2 as a door way to repeating the series with a new unit.

This led to being able to view units related to light in terms of light itself...
But then I noticed something about my series... It produced partitions.
I then learned that my infinite series of infinite series now resembles exactly Eulers partition function at level 4.
That wasn't my intention, I had created that by accident, and the way that I even realized I had found that, is by adding up the limits of this series... and it converged to a number given by Eulers function at 4... The only reason I learned that is because I compared my numerical value to known numerical values of experiments.

Then it got me thinking... If I was trying to measure the universe in terms of the universe itself.... what If I could use the same system to measure numbers compared to numbers themselves?

I started to think about the partitions as prime numbers, but not just any prime numbers, prime numbers organized into partitions which could follow the same logic of the Balmer series and split at level 2.

Doing this allowed me to view primes compared to twin primes, and also twin primes compared to cousin primes... and also, by extending the scale into the imaginary in the opposite direction, I was able to compare primes verse non primes, coming up with a specific ratio between them, which then if the prime series is infinite, then the following series would all become infinite as well.

That is my human level understanding of the system and how I arrived there.

I have organized the information into a paper using the actual math, with a lemma and clear terms.

I apologize that it is long, I was trying to be thorough and explicit.

The logic of it though is clear to follow and for those people who are well versed in Number theory I think you can probably skim the paper pretty fast and understand the concept.
The math itself is in the paper. {I updated this link to be the newest paper also, to avoid confusion. Older versions remain accessible in the revision history}

Grant I laughed so hard when I saw your video the first time, what a great riot that would have been. Maybe if I am lucky someday you and I can write a new song together about the primes.

Thanks for your time everyone.

Firstly I just want to say that I share the type of exuberance and wonder in my eyes that Grant does when he talks about this equation set.
I could spend hours just talking about and thinking about this equation, and how it relates to other equations.

Let me give you a couple examples of what I mean.

Lets imagine numbers were objects. What would their shape be? Would the number 4 be a square or would the number 4 be a 4 dimensional sphere? (pretty sure its the latter)

I argue that numbers are objects, and therefor they have properties.

I further argue that those shapes and properties must follow natural logic, and therefor equations that are automatically true must also apply to the logic of those objects.

For example if x= 1, then x^2 = x, that's purely logic based.

And if you think about it, If you have to start counting with a unit, you have to start somewhere. The place where you start would automatically be the boundary between an infinitesimal and zero. And since all numbers are self similar (1 is the same as 1, unless you give it different properties)
Then that means everything that comes after is built out of the same infinitesimals.

Therefor, due to the logical rule set I just stated, counting the integers is the same as counting the infinitesimals, starting with the smallest and moving upwards.
It's an infinite set of course, as the integers are.
And the difference between each number is that each number is basically just a shape. a shape of the boundary between existence and non existence.

I say these things to kick off the conversation for anyone who wants to chit chat with me about it.

I also wanted to point out, in the video Grant says "This is wrong if you view the two numbers as actual physical things, like a tiny nudge like a physicist" at 17:45 roughly

Here is my question: What does Grant really mean by this? Because what it sounds like he means is, a mathematician would call this a derivative, but a physicist wouldn't and we shouldn't disagree with physics because then we are most likely wrong

And If that's kind of the idea he is saying, I think that is 100% backwards. Physics should bow to mathematics or physics should leave the chat. Either physics is math, or it isn't. You can't have it both ways.

And here is why it's such an important topic for me.
I wrote a paper which is basically a grand unifying theory framework, and it is basically using the same equations Grant has here to construct particles and to show the fine structure constant and others come directly from these same circle and sphere relationships in higher dimensions.

Its not quite right I think, its so bloody close but I am just missing one concept that I havent figured out yet... I can show you the paper here

Edit {Its now correct, I actually found the bridge between QM and pure geometry. Its contained within the Balmer series , Here is the sucky paper I will improve on it tomorrow}

But mostly actually what I am interested in talking about is the concepts introduced in this video, and if there might be some other related equations hiding in the shadows, perhaps involving e or phi.

Just in general wanted to discuss this video though. Great video thanks Grant!

Edit [This video was also incredibly important, because it talks about projecting from 2D ->3D and 3D->4D]

Hi everyone, I am claiming to have formalized a proof for a Grand Unified Theory, but I am not here to talk about that, since that is too far off topic for this channel.

I am here to talk about how 3blue1brown and specifically this video helped me to understand the math well enough to solve this equation.

My whole life I struggled to understand the language attached to math. I could do amazing calculations in my head, and I could visualize incredibly detailed 3 dimensional structures in my mind, but the language of math was a huge barrier for me.

I didn't understand what a logarithm was, or a derivative.
However, I was already using those mathematical functions on a daily basis when designing neural network architecture and learning and loss functions.

I had never before heard of the Taylor series, and yet I had independently come up with the idea for using it as a back prop function. I don't remember if it worked as one or not, but I know that I tried it, without ever knowing it was called that.

3blue1brown videos changed my life. And specifically this video here. This is the video when I knew for certain in my heart it was the key concept in my proof.

It took me an additional 5 years or so I think, after watching this video to find the true answer, but this video was absolutely key.

This video taught me to view dimensions abstractly, and compare them mathematically, this allowed me to build the mathematical structure in my mind... and eventually I figured out how to create that structure mathematically that fully lines up pure number theory with pure physics.

I just want to say thankyou to Grant Sanderson, and everyone who helped make 3blue1brown happen.... I never would have been able to do it without your videos.

Someone invited me here not sure who, but here is a little about myself, and what I currently do.

I am an oldschool ai researcher, I've been working on Neural Network algorithms and architecture since before Deep neural nets were even a thing.

I have a vast and wide amount of experience regarding ai in general. I have been working independently to create some learning and loss functions based on geometry which are superior to the learning and loss functions used in standard LLM's

However, I realize that I will never be able to keep up with all of the Ai industry in the confines of my own basement.
Even though my algorithms are more efficient, I could never hope to compete with the amount of Compute that Open Ai can achieve.

And even though I am a smart guy, I am just one person, and it would take me decades to rebuild all of the functionality that Chat GPT already has if I was going to do it by myself.

So, I am looking for people to work with. For business partners perhaps.
Let's build something together.

Anyone in Edmonton? Let's talk. I know what we can build with this Ai that will change the world.