素数分布和筛法均是解析数论中的重要问题。本项目将主要研究Shapiro型素数以及可表示为一元高次多项式型殆素数的相邻间隔差问题，所涉及的主要工具就是筛法。对于Shapiro型素数，本项目主要致力于它的小差问题和大差问题以及孪生Shapiro型素数问题。对于可表示为一元高次多项式型殆素数，本项目致力于研究弱化的A.Schinzel猜想，也就是殆素数型版本及相关的殆素数型相邻差问题。

The distribution of primes and sieve method are all the important problems in analytic number theory. In this project, we will study the gaps between of Shapiro primes and the almost-primes can be written by higher polynomial in one variable. For Shapiro primes, this project focus on the small gaps and large gaps between Shapiro primes and twin Shapiro primes. For the almost-primes can be written by higher polynomial in one variable, this project studies the weaker A.Schinzel conjecture, it means the A.Schinzel conjecture for almost-primes and related problems for the difference between of this type almost-primes.