On the prime distribution

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 $A_1,A_2,\dots ,A_i.\dots$, 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.

16 pages