本项目主要围绕下述三类堆垒数论问题开展定量研究：（1）借鉴Helfgott近期完全"移除"三素数定理中"充分大"条件，从而完整解决奇数Goldbach猜想的思想，寻求移除一些非线性低方幂素变数方程可解性对于"充分大"条件的依赖，比如移除华罗庚先生五平方素数定理中的"充分大"条件等。（2）结合近期算术组合和零点分布的有关研究及进展，继续研究Dirichlet L函数零点分布和密度估计的定量估计，进而考虑Linnik-Gallagher型方程最小素数解的定量上界估计，并继续考虑Baker关于素变数方程解的定量上界估计。（3）结合张益唐对孪生素数猜想的重大推进及Maynard等人的相关跟进，考虑有关均值定理的推广改进和应用，进而通过细化Maynard对Goldston-Pints-Yildirim型筛法的推广，探讨某些相关定量结果的直接改进和有关延伸。

The purpose of this project is to give some quantitative studies related to the following three kinds of problems in the field of additive prime number theory. (1)Consider to remove the "sufficiently large"condition in the results of expressing integers as sums of lower prime powers,such as that in the classical theorem of professor Hua that every "sufficiently large" integer congruent to 5 modulo 24 is a sum of five prime squares.The investigation of these kinds of problems is interesting and valuable if one notes and compares it with a recent important result of Helfgott,which gave a complete solution to the classical odd Goldbach conjecture. (2)Using the latest numerical results in the field of arithmetic combinatorics and zeros of Dirichlet L functions, we continue to consider the numerical upper bound of the least prime solution of some Linnik-Gallagher equations, and consider the improvement of Baker's constant on the upper bound of solution of some equations with prime variables. (3)By some delicate investigation of the ideas and the methods of Yitang Zhang and James Maynard,we manage to discuss some related new kinds of mean value theorems,and then by considering the sieve of Goldston-Pints-Yildirim, we come to give some new quantitative results on the related problems,such as the prime twin conjecture itself.