Number Theory

    

On the Prime Distribution

Authors: Yong Zhao, Jianqin Zhou

In this paper, the estimation formula of the number of primes in a given interval is obtained by using the prime distribution property. For any prime pairs $p>5$ and $ q>5 $, construct a disjoint infinite set sequence $A_1, A_2, \ldots, A_i. \ldots $, such that the number of prime pairs ($p_i$ and $q_i $, $p_i-q_i = p-q $) in $A_i $ increases gradually, where $i>0$. So twin prime conjecture is true. We also prove that for any even integer $m>2700$, there exist more than 10 prime pairs $(p,q)$, such that $p+q=m$. Thus Goldbach conjecture is true.

Comments: 16 Pages.

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Submission history

[v1] 2021-10-30 18:43:21
[v2] 2021-11-10 03:33:24

Unique-IP document downloads: 313 times

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