On the prime distribution

2021/10/28 by Yong Zhao, Zhao, Yong, Jianqin Zhou +1
Mathematics · #11N05 #11P32 #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.2110.15014

openalex publication_date 2021/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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>5 and q>5 , construct a disjoint infinite set sequence A₁, A₂, …, A_i. … , 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.

Related

• Characterization of the Distribution of Twin Primes
• Goldbach and Twin Prime Pairs: A Sieve Method to Connect the Two
• The Set-Theoretic Form of Twin Prime Distribution and Its Odd-Even Imbalance
• Definitive Proof of Goldbach's conjecture
• A new enlightenment about gaps between primes