因数个数函数与素数的方程筛
The Functions on the Submultiple Quantity and Equations of Prime Sieve
摘要:
本文定义的因数个数函数是用于表达任意一个自然数中所包含因数的数量的函数。创立一个脉冲函数I，把任一个自然数的因数个数表达为一系列I之和，可以推出因数个数函数的解析表达式。进而，从因数个数函数的定义出发又导出因数个数函数的解析表达方式有无限多个，可组成因数个数解析函数族。本文定义了素数的方程筛，并提出可用因数个数函数构造方程筛，以及用方程筛证明哥德巴赫猜想的思路。用方程筛作为证明素数命题的工具，其优点是回避或减少了逻辑判断，缺点是表达式较长。
Abstract:
The functions on submultiple quantity (abbreviated as FSQ),which is defined here, is used to count submultiple quantity of the natural numbers. Creating a pulse function I, submultiple quantity of every natural number may be represented by the sum of a series of I, then the analytic formula of FNS can be lead to. And from the definition of FSQ, it can be derived that the quantity of the analytic formulas of FSQ is unlimited and can form family of functions. Finally the equation sieve of prime number is defined and it can be formed by FNS, and then a way to prove Goldbach conjecture is opened. The advantage of using the equation sieve as a tool of solving prime problem is that the logical judgment can be avoided or reduced; but the disadvantage is that the formula is relatively complicated.