Number Theory

    

The Unity of the Prime Number Theorem, Bertrand's Postulate and Euler's Proof

Authors: Yong Zhao

For any integer n greater than 1 such that 2n+1 is prime, we construct interval (n,2n). By synthesizing the prime number theorem, the Bertrand—Chebyshev theorem and Euler's proof to analyze the gap between 2n+1 and primes in the interval (n,2n), we prove the Polignac's Conjecture.For any integer greater than 1, we construct intervals (n,2n) and (2n,4n). By synthesizing the Bertrand—Chebyshev theorem and the prime number theorem to analyze the gap of primes between the consecutive intervals, we prove the Polignac's Conjecture.

Comments: 4 Pages.

Download: PDF

Submission history

[v1] 2026-09-08 06:47:50

Unique-IP document downloads: 0 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus