A concise proof of Goldbach conjecture and hardy-littlewood prime sum conjecture

A concise proof of the Goldbach Conjecture and the Hardy-Littlewood Prime Sum Conjecture are given in this paper. The core idea of this paper is to transform the problem of representing an integer as a sum of several primes into counting the number of integer solutions of the corresponding Diophantine equation. Firstly, the combinatorial approximation method to compute the approximate number of integer solutions to linear Diophantine equation with integer subsets (prime number) as solution set is presented. Secondly, the approximate number of integer solutions of Chen Jingrun's "1+2" theorem and Vinogradov's theorem of sum of three primes are computed to validate the combinatorial approximation method. Finally, the approximate number of integer solutions of the Goldbach (equation) Conjecture and the Hardy-Littlewood Prime Sum (equation) Conjecture are computed and the results we obtained are consistent with the conjecture, thus proof of the Goldbach Conjecture and the Hardy-Littlewood Prime Sum Conjecture are provided.