关于某些特殊类型的素数的无限性
On the Infinitude of Some Special Kinds of Primes
摘要：
本文的目的是试图建立一个通用模型的问题，多个多元数论函数同时表示素数的无穷多个整点。更具体地说，我们简要介绍了从欧几里德第二定理到格林-陶定理的研究背景--历史和现状。本文分析了整系数不可约一元多项式表示无穷多个素数的等价必要条件，找到了可能暗示费马素数只存在无穷多个的新的必要条件，得到了孙子剩余定理、广义欧拉函数、素数计数函数和Schinzel-Sierpinski猜想等的类比。这只是一个开始，还有很长的路要走。我们希望数论学家进一步考虑它。
英文摘要：
The aim of this paper is to try to establish a generic model for the problem that several multivariable number-theoretic functions represent simultaneously primes for infinitely many integral points. More concretely, we introduced briefly the research background-the history and current situation-from Euclid's second theorem to Green-Tao theorem. We analyzed some equivalent necessary conditions that irreducible univariable polynomials with integral coefficients represent infinitely many primes, found new necessary conditions which perhaps imply that there are only finitely many Fermat primes, obtained an analogy of the Chinese Remainder Theorem, generalized Euler's function, the prime-counting function and Schinzel-Sierpinski's Conjecture and so on. Nevertheless, this is only a beginning and it miles to go. We hope that number theorists consider further it.
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。
