用一种新的素数${P_{N}}$后素数${P_{N+1}}$的求法证明孪生素数猜想及对最大有界素数间隔${G_{i}}$的改进
Towards Proving the Twin Prime Conjecture using a Novel Method For Finding the Next Prime Number ${P_{N+1}}$ after a Given Prime Number ${P_{N}}$ and a Refinement on the Maximal Bounded Prime Gap ${G_{i}}$
摘要：
本文介绍了一种求给定素数${P}$后的下一个素数的新方法。所提出的方法是用来推导出一个系统的不等式，作为约束，应满足的所有素数，其继任者是一个孪生素数。孪生素数是素数间隔为${2}$的素数。对${(5,7),(11,13),(41,43)}$等等都是孪生素数。本文设想，如果所提出的不等式组可以被证明有无穷多个解，孪生素数猜想将被证明是正确的。本文还导出了一个新的上界的素数差距，${G_{i}}$之间的${P_{i} \; and \; P_{i+1}}$，作为${P_{i}}$的函数。
英文摘要：
This paper introduces a new method to find the next prime number after a given prime ${P}$. The proposed method is used to derive a system of inequalities, that serve as constraints which should be satisfied by all primes whose successor is a twin prime. Twin primes are primes having a prime gap of ${2}$. The pairs ${(5,7),(11,13),(41,43)}$, etcetera are all twin primes. This paper envisions that if the proposed system of inequalities can be proven to have infinite solutions, the Twin Prime Conjecture will evidently be proven true. The paper also derives a novel upper bound on the prime gap, ${G_{i}}$ between ${P_{i} \; and \; P_{i+1}}$, as a function of ${P_{i}}$.
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。
