素数堆垒问题是丢番图方程和素数分布这两个数论重要研究领域的交叉领域，具有重要的理论意义。.本项目的主要研究内容是：一、继续关注经典解析方法和经典问题，尤其是圆法和筛法对素数堆垒问题的重要作用，系统研究不等次幂华林-哥德巴赫问题，给出一般性的结果；寻找更多的Goldbach-Linnik型分拆式；二、深入研究Linnik方差法，使其成为研究素数堆垒问题的新方法，为四素数平方和猜想的最终证明提供阶段性结果；三、探讨三次及以上一般丢番图方程素数解的结构，证明Sarnak猜想在素数堆垒问题上的特例，为Sarnak猜想提供更多实证。.计划通过本项目的实施，将Linnik方差法的新技术与经典解析方法相结合，在素数堆垒问题研究领域取得有影响的原创性成果。.本研究课题与已引起普遍关注的Sarnak猜想研究具有密切的联系，属于解析数论领域的热门课题和前沿课题。

The research on the theory of additive problem of prime numbers is an interdisciplinary study field, which covers two of the most important fields in number theory, the distribution of primes and Diophantine equations. Therefore, The research on this topic is of great theoretical significance. .This research includes: (1) We will continue to pay attention to classical analytic methods and classical problems, especially the important role of circle method and sieve methods to the theory of additive problem of prime numbers. We will research Waring-Goldbach problem for unlike powers systematically, and give some general results. We will look for more Goldbach-Linnik type partitions. (2) The Linnik dispersion method will be studied in depth, which makes it a new method to study the theory of additive problem of prime numbers. This will lead to get some important progress of the final proof of the four-prime-squares-conjecture. (3) We will discuss the structure of prime solutions of general Diophantine equations with degree three or more, and give the proof of some special cases of Sarnak conjecture on additive problem of prime numbers, which provides more evidences for Sarnak conjecture..Through this project, we plan to combine the new technology of Linnik dispersion method, with classical analytic methods in order to get some influential original results in the field of additive problem of prime numbers..It should be pointed out that there is a close relation between this project and the Sarnak conjecture which has been attracting increasing attentions recently. Therefore, this project is a popular research standing at the frontier of analytic number theory.