English

On the prime distribution

General Mathematics 2021-11-09 v2

Abstract

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>5p>5 and q>5 q>5 , construct a disjoint infinite set sequence A1,A2,,Ai.A_1, A_2, \ldots, A_i. \ldots , such that the number of prime pairs (pip_i and qiq_i , piqi=pqp_i-q_i = p-q ) in AiA_i increases gradually, where i>0i>0. So twin prime conjecture is true. We also prove that for any even integer m>2700m>2700, there exist more than 10 prime pairs (p,q)(p,q), such that p+q=mp+q=m. Thus Goldbach conjecture is true.

Keywords

Cite

@article{arxiv.2110.15014,
  title  = {On the prime distribution},
  author = {Yong Zhao and Jianqin Zhou},
  journal= {arXiv preprint arXiv:2110.15014},
  year   = {2021}
}

Comments

16 pages

R2 v1 2026-06-24T07:15:38.383Z