The prime distribution Theorem

Biblioteka greatest integer function. This is called the prime distribution theorem. And by the theorem, we can completely prove a series of conjectures as follows: Oppermann’s conjecture, Legendre’s conjecture, Andrica conjecture, Brocard’s conjecture etc.I hope this paper is suitable for your famous journal. The attachment includes an pdf file of the paper (the prime distribution theorem and application.pdf); Web-submission Please acknowledge the receipt of my submission at your convenient time. Looking forward to hearing from you sooner. With Best Regards Sincerely Yours Wan Guoqiang
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1, 2, 3, 4, 5; 6, 7, 8, 9, 10; 11, 12, 13, 14, 15; 16, 17, 18, 19, 20; 21, 22, 23, 24, 25; 26, 27, 28. We call every equal share a complete chunk. The last share is called a broken chunk. Sometimes the last share may also be a complete chunk. For example: The equal share 1, 2, 3, 4, 5; 6, 7, 8, 9, 10; 11, 12, 13, 14, 15 etc are complete chunks. The share 26, 27, 28 is a broken chunk. Observing the given sequence, we find that there is at least one prime every complete chunk. This is not an accidental phenomenon, but an inevitable rule. Remark: 1. the 1th chunk must start with the number 1. 2. May or may not have the prime in the broken chunk. 3. Let Ari denote the set that contains the true elements of the multiples of pi in the r-th chunk, where pi is the i-th prime. Let Bri denote the set that consists of the maximum elements of the multiples of pi in the r-th chunk, where pi is the i-th prime. For instance: Let A11 denote the set that contains the true elements of the multiples of 2, where 2 is the 1-th prime in the 1-th chunk. Let B11 denote the set that contains the maximum elements of the multiples of 2, where 2 is the 1th prime in every chunk. Assume that there are three elements of the multiples of 2 in the set B11 . So
⎡ 28 ⎤ A11 = {2, 4} ⊂ B11 , A11 < B11 = ⎢ ⎥ +1 = 3 . ⎣ 2 ⎦
By the same way, we get
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⎡ 28 ⎤ A21 = {6,8,10} = B21 , A21 = B21 = ⎢ ⎥ +1 = 3 . ⎣ 2 ⎦
The prime distribution Theorem
Cover Letter
Prof. Dr. David Goss International Journal of Number Theory Email: 408073346@ Submission my paper to International Journal of Number Theory February 4, 2013 Dear Prof. Goss I hope everything goes well with you. I am very happy to have the chance of submitting my recent work entitled as The Prime Distribution Theorem to your highly esteemed journal- International Journal of Number Theory. I confirm that this paper is original, neither partly nor wholly has been published anywhere in any forms, this paper is not under review by another journal, and I will not re-submit it to another journal or a conference during the reviewing procedure. In this paper, we present a theorem about the distribution of the prime numbers. That is, there is at least one prime every n consecutive integers from 1 to n, where n is called the
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Legendre’s
Andrica conjecture,
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Brocard’s conjecture
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etc.
Keyword: Prime, Prime distribution, Oppermann’s conjecture, Legendre’s conjecture, Andrica conjecture, Brocard’s conjecture. We begin with a simple example. Given a sequence of the consecutive positive integers from 1 to 28, we divide the sequence into shares by ⎡ 28 ⎤ = 5 .
The Prime Distribution Theorem.
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If we divide a sequence of the consecutive
positive integers from 1 to n into chunks by ⎡ n ⎤ then there is at least one prime every
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the greatest integer function. It is called the prime distribution theorem. And by the theorem, we can completely prove a series of conjectures as follows: Oppermann’s conjecture, conjecture,
*Manuscript Click here to view linked References
The Prime Distribution Theorem and Application
Author: Wan Guoqiang
E-mail：408073346@
Abstract: In this paper, we present a theorem about the distribution of the prime numbers. That is, there is at least one prime every ⎡ n ⎤ consecutive integers from 1 to n, where ⎡ n ⎤ is called
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complete chunk, where n ≥ 4 . Proof. Let Ari denote the set that contains the true elements of the multiples of pi in the r-th chunk, where pi is the i-th prime and r ≤ ⎡ n ⎤ . Suppose that Bri denotes the set that
Elsevier Editorial System(tm) for Journal of Number Theory Manuscript Draft Manuscript Number: JNT-D-13-00055 Title: The Prime Distribution Theorem and Application Article Type: Full Length Article Keywords: Prime, Prime distribution, Oppermann's conjecture, Legendre's conjecture, Andrica conjecture, Brocard's conjecture. Corresponding Author: Mr. Wan Guoqiang, Corresponding Author's Institution: First Author: Wan Guoqiang Order of Authors: Wan Guoqiang; Wan Guoqiang Abstract: In this paper, we present a theorem about the distribution of the prime numbers. That is, there is at least one prime every consecutive integers from 1 to n, where is called the greatest integer function. It is called the prime distribution theorem. And by the theorem, we can completely prove a series of conjectures as follows: Oppermann's conjecture, Legendre's conjecture, Andrica conjecture, Brocard's conjecture etc.