关于素数集合的代数结构
On algebraic structure of the set of prime numbers
摘要：
根据素数的代数结构和算术结构，对素数集进行了分析。本文通过对素数集合的一种线性公式的推导，重新定义和识别了它们，并在系统的程序下证明了素数集合是具有更多初等结构的自然数的某些子集的组合（并和交）。实际上，一般来说，所得到的素数公式的逻辑实质与奇数公式2n - 1类似，以此类推，利用所得到的公式可以定义所有的合数。最后给出了具体算例。
英文摘要：
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has been shown that the set of prime numbers is combinations (unions and intersections) of some subsets of natural numbers, with more primary structures. In fact generally, the logical essence of obtained formula for prime numbers is similar to formula 2n - 1 for odd numbers, and so on. Subsequently, using obtained formula we can define all composite numbers. Finally specified examples for obtained formula are presented.
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。
