  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.
