哥德巴赫问题的筛选函数剖分
Sifting Function Partition for the Goldbach Problem
摘要：
哥德巴赫问题的所有筛法都筛选出所有的合数;尽管严格地说，没有必要这样做，而且这通常是非常困难的。本文介绍的几种新方法表明，哥德巴赫问题可以在只筛选出某些合数的情况下求解。事实上，要证明哥德巴赫猜想，只需要证明初始筛选后的剩余整数中还剩下素数就可以了！这一思想可以分别用整数排序筛选函数划分法、区间筛选函数划分法和比较筛法三种方法中的一种来实现。这些都是解决哥德巴赫问题和孪生素数问题的可行方法。上述方法的额外好处是消除了筛选函数的上界和下界所带来的不确定性。
英文摘要：
All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so and which is, in general, very difficult. Some new methods introduced in this paper show that the Goldbach problem can be solved under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can be implemented by using one of the three methods called sifting function partition by integer sort, sifting function partition by intervals and comparative sieve method, respectively. These are feasible methods for solving both the Goldbach problem and the problem of twin primes. An added bonus of the above methods is the elimination of the indeterminacy of the sifting functions brought about by their upper and lower bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
