What to do now. Prime number distribution solved

Feb 2020
62
1
St Louis
Hello, my name is Pat. I am new here and have a question.
I don't know how I should start with this, or how this will be received, but here goes.



On December 12, 2019, I thought I would take a crack at something. Something that seemed so simple on the outside. Little did I know at that time that what I was about to do would have me asking the very nature of things and where they came from. and down this rabbit hole I went. not knowing that the something I sought was itself everything, and that everything.was contained in the number itself.

And as it was, I began research on the distribution of prime numbers.
After 7 days of actually working on this problem, I discovered something.... very interesting.
That something was a structure, a pattern.

And that day was Christmas.
Literally.

Since then I have spent every day doing further research, trying to put a hole in it, or find something similar.
I can not.
I looked all over the internet and spent days at the downtown library, going through every book on mathematics they had. In rare cases, some came close, but the numbers were wrong, the operation was represented, and the pattern was completely overlooked or ignored.

When others saw nothing, I saw the beauty. I assure you that everything is beautiful.

As of today, I have been developing a software that uses this pattern to generate primes while providing the factors of others. Again, this a simple process that involves no division, but I have not found a way to formulate it as the formal equation for what I am doing seemingly does not exist.


I can tell you with absolute certainty whether n is prime without the use of division.....

But I have not found a way to express it. How does one just start making up symbols and inventing math? Or am I missing some form of math that does exist? I doubt the latter, as I have been around and around in circles leading to the same branches of mathematics, that seems to be underdeveloped. This is surprising as the process that I am seeking to describe is quite simple from the outside.

I know that I have not told you the process in detail, as I have yet to present it. and that is my question. Where do I go from here with this? Some people I have spoke with say that I need to patent what I have done, as it is a "process" that "produces" or "manufactures" something, but I am still not sure as to whether such a thing can be done. Patent math??
I have also been studying recently about RSA encryption, and i believe one can very easily develop a program that can factor these very large numbers in minutes if not seconds (as well as all the numbers that come before if I wanted to). Again, this is all done without division. Simple enough a smartphone could do it.

But again, what steps do I need to take to bring this discovery to light? I do not want the credit of my work to go to someone else. And yes. I want the money too.

And then there is this.
the EFF Cooperative Computing Awards

\$150,000 to the first individual or group who discovers a prime number with at least 100,000,000 decimal digits
\$250,000 to the first individual or group who discovers a prime number with at least 1,000,000,000 decimal digits
I can do this right now, but the rules state that how I do it (the process) needs to be accepted by the mathematical community, because as of today the ONLY accepted (known) way is by trial division.


I have reached out to 2 local universities with no response, other than one physicist that had me conclude that established mathematicians would not be so very happy that someone from the "outside" figured this one out, and that I would not be taken seriously. However, what I have done is irrefutable. It can be looked at as an Axiom.


Some may be thinking.. as to the Riemann Hypothesis, and the zeta function.....
(the infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ....= -1/12)
I believe what I have found can rationalise this statement.

__________________________________________________________________________

Thank you for taking your time reading this.
Any help of guidance you could give with this is very appreciated.
Guest
 

topsquark

Math Team
May 2013
2,524
1,049
The Astral plane
There is a pattern to the primes. You can determine if any number is prime using the sieve of Erostothenes.

So, just for the sh!ts and giggles of it, is 984759465937503850398458375936586395730583088282075936596393085003094573045803984039680736047304683089603984603749673085330495803985037603974053 a prime number? If not, please provide how you find the factors. (You are on your honor to not use a calculation device such as W|A.)

As to \(\displaystyle \zeta (-1)\) the problem is done by analytic continuation. That's how you "rationalize" the statement.

-Dan
 
Feb 2020
62
1
St Louis
I will say this: what I am doing is not a sieve.
The number you gave seems as though it is not Prime, as the sum of all its digits= a multiple of 3. I did not use what I have found to verify this. As I said, I am only in the developmental stages of the programing.

Without the use of analytic continuation, I can tell you that the pattern in the sequence of all real numbers, repeats itself in respect to 12.
3,6,and 9 play a key role in that pattern.
Hint: why do we have highly composite numbers and why are they that way? What makes the position of these numbers unique? I can tell you when and how the pattern repeats itself.

edit.. the funny thing is that the sum of the digits of the number you gave is 693
 
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topsquark

Math Team
May 2013
2,524
1,049
The Astral plane
I will say this. what i am doing is not a sieve.
the number you gave seems as though it is not Prime, as he sum of all its digits= a multiple of 3. i did not use what i have found to verify this, as i said i am only in the developmental stages of the programing.

Without the use of analytic continuation, I can tell you that the pattern in the sequence of all real numbers, repeats itself in respect to 12.
3,6,and 9 play a key role in that pattern
hint: why do we have highly composite numbers and why are they that way? what makes the position of these numbers unique? i can tell you when and how the pattern repeats itself.

edit.. the funny thing is that the sum of the digits of the number you gave is 693
As to the factoring, okay, but you really shouldn't advertise it if you haven't finished the work. So could you explain your method?

\(\displaystyle \sum_{n = 1}^{\infty} n = -\dfrac{1}{12}\) is an absolutely silly statement as all the terms in the sum are positive and bigger than 1/12. The formula to compute \(\displaystyle \zeta (-1)\) cannot be done using real numbers. (Never mind the fact that you see \(\displaystyle \sum_{s = 1}^{\infty} n = -\dfrac{1}{12}\) written all over the place.)

-Dan
 
Feb 2020
62
1
St Louis
As to the factoring, okay, but you really shouldn't advertise it if you haven't finished the work. So could you explain your method?

\(\displaystyle \sum_{n = 1}^{\infty} n = -\dfrac{1}{12}\) is an absolutely silly statement as all the terms in the sum are positive and bigger than 1/12. The formula to compute \(\displaystyle \zeta (-1)\) cannot be done using real numbers. (Never mind the fact that you see \(\displaystyle \sum_{s = 1}^{\infty} n = -\dfrac{1}{12}\) written all over the place.)

-Dan
I will not go into the details of my method before my work is published.
However, I can tell you the methodology is sound and it applies to not just some primes but to all of them, to any given number with absolute certainty. Explaining it mathematically, however, is where I am stuck. It's like mathematics was leaping forward so fast that certain "simple" things that seemed unimportant to whoever at the time, were left underdeveloped. I have full belief that once I find a way the best way to explain it in mathematical terms, what is going on, many other formulas will come from it. the prime number theorem for example. π(x) an approximate answer, it is possible that one could achieve an exact answer from my method.

I am not trying to advertise my work. I am simply asking what steps do one take to make this all come to fruition. How does one get published in a journal without having a career in the subject? Is it necessary to patent the method/process, or is that even possible? All I know is that I have to reach out to those that do know, and that want to know. I am by no means a professional mathematician. It would be a dam shame if this gets thrown in the desk and forgotten because everyone was too selfish and arrogant to listen to someone from the outside. I understand that claims are made all the time.. but this is not the case here. i didn't find some trivial little thing. this applies to everything. identifying what they are and how they are

without division. <----- and that part right there, yea that.
 

topsquark

Math Team
May 2013
2,524
1,049
The Astral plane
In your case, you'd probably want to try for ArXiv. They are a pre-print service and I know there is some peer review, but I don't know whether it is as rigorous as if you went to a more traditional journal. In your case, with you not having a degree in the subject, they would almost certainly review your work. You will need to do a very good write up and my best suggestion is that you are going to need a partner that does have a degree (and is willing to keep you as the primary author) to work with you on the details, so your secrecy policy is going to have to be broken at some point.

-Dan
 
Feb 2020
62
1
St Louis
In your case, you'd probably want to try for ArXiv. They are a pre-print service and I know there is some peer review, but I don't know whether it is as rigorous as if you went to a more traditional journal. In your case, with you not having a degree in the subject, they would almost certainly review your work. You will need to do a very good write up and my best suggestion is that you are going to need a partner that does have a degree (and is willing to keep you as the primary author) to work with you on the details, so your secrecy policy is going to have to be broken at some point.

-Dan
Thank you for your response.
I am aware of the partnership aspect, and i know i could use the help. Trusting someone that I don't know is a hard pill to swallow.
I have had to learn more about math in two months than i ever expected. it wasn't necessary to find the pattern, only to find a way to describe it. I love the fact that i can now read and understand the equations I look at. 2 months ago, it all looked like greek, lol
I have just started the process of reaching out to different people through venture cafes and such, as I need funding for the various commercial applications, (another aspect i need to research further)
I really don't know of all the real world applications. That wasn't the driving force when I started.
I know of some scientists (one in particular) that have written many articles on the subject matter pertaining to the method I am using. The math is defined well for the applications they use it for, but I guess i am reengineering their work to fit what i am doing.
Still haven't got an answer as to patenting of it either.

again thank you.
 

topsquark

Math Team
May 2013
2,524
1,049
The Astral plane
Still haven't got an answer as to patenting of it either
No one gets patents in the Sciences and Mathematics. You aren't producing any sort of a product. All you get is acclaim for solving the problem.

And if you are lucky they might name the method after you.

-Dan
 
Feb 2020
62
1
St Louis
You can't patent math.



The whole thing crazy.
The Federal Circuit decision that opened the software patent floodgates was In Re Alappat, which was decided in 1994. In that case, the Federal Circuit allowed a patent on the use of anti-aliasing to improve the display of a digital oscilloscope. It ruled that "a general purpose computer in effect becomes a special purpose computer"—and therefore is eligible for patent protection—once it's loaded with a specific computer program.

The Federal Circuit insists it hasn't changed this rule. "We have never suggested that simply reciting the use of a computer to execute an algorithm that can be performed entirely in the human mind falls within the Alappat rule." This implies that a human being couldn't perform the anti-aliasing techniques described in the Alappat patent, but that's simply wrong. The math involved is little more than basic geometry.

More importantly, exactly the same point applies to both of the software patents the Supreme Court rejected in the 1970s. As the Supreme Court put it in 1972: "The mathematical formula involved here has no substantial practical application except in connection with a digital computer." Theoretically, you could have performed the calculations with a pencil and paper, but no one actually did so. Yet the Supreme Court still held them to be unpatentable mental processes.
 
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