Hello, I am looking for people who are skilled in mathematics so that they can help me in the development of this subject and if there is a problem, they can correct it.
I know that in the previous post, there was a lot of controversy and discussion, but in this post, I was not biased, so you can be completely sure that this post and its content have been reviewed more than several times to avoid false biases.
In the previous post a bit of bias led me off track I'm still working on this issue, but you won't see anything new in the post until further notice.
Let's start from the beginning, it's been a while since I posted the previous post, but it doesn't matter that after that I decided to start reading a novel. I chose one of Hemingway's novels. After reading a few pages, I got bored and I went to YouTube and looked for 3Blue 1Brown and saw one of his videos, after reading the Fourier Series article on Wikipedia, I thought why not make a function that can generate prime numbers, even though I knew everyone was saying something like that. It's not possible because the pattern of prime numbers is not fixed and the algorithm and functions mostly depend on the stability, but still, I started my work.
Step one: Oscillation
Oscillation is one of the properties of trigonometric functions, and periodicity is the same, these properties also apply to prime numbers, but the big difference between the periodicity of trigonometric functions and prime numbers is that prime numbers do not have a fixed periodicity and a proportional value for the change and the distance between There are no numbers, but there are for trigonometric functions.
The first point is that we have to mix this frequency in a way, yes! discrete; Discrete functions are functions that are not differentiable, which means that they have periodicity, but the interval between each oscillation is different from the previous interval, and this also means that they are not continuous.
Sine and cosine are functions that by themselves have a periodicity equal to the number of pi, that is, the frequency of the wave is pi every time, that is, in the first oscillation of pi, the square becomes two times 2, and so on.
Now, instead of changing the type of distribution of sine and cosine waves, we have to move them and take them in another direction, but at the same time we have to mix the periodicity and this is only possible by changing the type of wave distribution, so it is better to divide the wave.
For now, we will refrain from presenting the numbers, but the main formula will be shown below.
Step Two: Globalization
How can we be sure that we will have all the prime numbers, yes! With the help of large operations and in this regard adding numbers.
First, we have to put all the main formula that we had for mixing the periodicity and changing the position of the wave in one sum, the lower limit is zero and the variable upper limit of the input of the function, and now we have the function:
[math]f\left(x\right)=\sum_{n=0}^{x}\left(n+\sin\left(\frac{\left(2n\pi x-1\right)}{3}\right)-\frac{\cos\left(2\pi nx\right)}{n+2\pi}\right)[/math]You may protest and say where did you get this relationship, you are right, I came to this by playing with the elements and properties that I was looking for, and of course, this is a function of things that should be a function of our producer. Let me show you by displaying the graph of this function in Desmos, the image is attached to the post.
If you have seen the picture, you will say that we have not seen the actual formula display, but you have given the sine x function to the variable and graphed it.
Well, you are right, but we said that we need periodicity, and if you display this formula yourself without quantization, you will see that it still has periodicity, but the disorder that exists does not bring our fluctuations, because this function by itself The upper side moves forever and this has caused the property of capturing all prime numbers to be lost, so sine must be used to show all the values and observe the desired fluctuations.
Beta means that the function is discrete, but at least we have the periodicity that might collapse due to the discontinuity, and from negative numbers to positive numbers, we have prime numbers, and the prime numbers are the points of the roots of the function curve, which you can click on You can see that the root is a combination of pi and x, and this ordered pair has y along with it. Of course, if the root was only on the x-axis, we would not have y, but if it was not on the x-axis, this ordered pair exists, but now in This ordered pair of elements of x is a prime number!
Now leave the wondering for later, let's focus on the problems.
1 - After the number 13, this function no longer has the original periodicity of prime numbers, but it still produces prime numbers.
2 - The function is long and long and there is no way to shorten it, because if we short it all the properties get gone.
3 - We need to find a way to set the function so that it doesn't need to be displayed so that we can find the numbers
4 - The main reason for the production of prime numbers is not yet known, or at least to me
5 - This function is understandable for a few people and if someone wants to understand it, he must have done a lot of education.
Please feel free and respectfully share any comments you have.
I know that in the previous post, there was a lot of controversy and discussion, but in this post, I was not biased, so you can be completely sure that this post and its content have been reviewed more than several times to avoid false biases.
In the previous post a bit of bias led me off track I'm still working on this issue, but you won't see anything new in the post until further notice.
Let's start from the beginning, it's been a while since I posted the previous post, but it doesn't matter that after that I decided to start reading a novel. I chose one of Hemingway's novels. After reading a few pages, I got bored and I went to YouTube and looked for 3Blue 1Brown and saw one of his videos, after reading the Fourier Series article on Wikipedia, I thought why not make a function that can generate prime numbers, even though I knew everyone was saying something like that. It's not possible because the pattern of prime numbers is not fixed and the algorithm and functions mostly depend on the stability, but still, I started my work.
Step one: Oscillation
Oscillation is one of the properties of trigonometric functions, and periodicity is the same, these properties also apply to prime numbers, but the big difference between the periodicity of trigonometric functions and prime numbers is that prime numbers do not have a fixed periodicity and a proportional value for the change and the distance between There are no numbers, but there are for trigonometric functions.
The first point is that we have to mix this frequency in a way, yes! discrete; Discrete functions are functions that are not differentiable, which means that they have periodicity, but the interval between each oscillation is different from the previous interval, and this also means that they are not continuous.
Sine and cosine are functions that by themselves have a periodicity equal to the number of pi, that is, the frequency of the wave is pi every time, that is, in the first oscillation of pi, the square becomes two times 2, and so on.
Now, instead of changing the type of distribution of sine and cosine waves, we have to move them and take them in another direction, but at the same time we have to mix the periodicity and this is only possible by changing the type of wave distribution, so it is better to divide the wave.
For now, we will refrain from presenting the numbers, but the main formula will be shown below.
Step Two: Globalization
How can we be sure that we will have all the prime numbers, yes! With the help of large operations and in this regard adding numbers.
First, we have to put all the main formula that we had for mixing the periodicity and changing the position of the wave in one sum, the lower limit is zero and the variable upper limit of the input of the function, and now we have the function:
[math]f\left(x\right)=\sum_{n=0}^{x}\left(n+\sin\left(\frac{\left(2n\pi x-1\right)}{3}\right)-\frac{\cos\left(2\pi nx\right)}{n+2\pi}\right)[/math]You may protest and say where did you get this relationship, you are right, I came to this by playing with the elements and properties that I was looking for, and of course, this is a function of things that should be a function of our producer. Let me show you by displaying the graph of this function in Desmos, the image is attached to the post.
If you have seen the picture, you will say that we have not seen the actual formula display, but you have given the sine x function to the variable and graphed it.
Well, you are right, but we said that we need periodicity, and if you display this formula yourself without quantization, you will see that it still has periodicity, but the disorder that exists does not bring our fluctuations, because this function by itself The upper side moves forever and this has caused the property of capturing all prime numbers to be lost, so sine must be used to show all the values and observe the desired fluctuations.
Beta means that the function is discrete, but at least we have the periodicity that might collapse due to the discontinuity, and from negative numbers to positive numbers, we have prime numbers, and the prime numbers are the points of the roots of the function curve, which you can click on You can see that the root is a combination of pi and x, and this ordered pair has y along with it. Of course, if the root was only on the x-axis, we would not have y, but if it was not on the x-axis, this ordered pair exists, but now in This ordered pair of elements of x is a prime number!
Now leave the wondering for later, let's focus on the problems.
1 - After the number 13, this function no longer has the original periodicity of prime numbers, but it still produces prime numbers.
2 - The function is long and long and there is no way to shorten it, because if we short it all the properties get gone.
3 - We need to find a way to set the function so that it doesn't need to be displayed so that we can find the numbers
4 - The main reason for the production of prime numbers is not yet known, or at least to me
5 - This function is understandable for a few people and if someone wants to understand it, he must have done a lot of education.
Please feel free and respectfully share any comments you have.
Attachments
Last edited by a moderator: