Application of the Inclusion-Exclusion Principle to Prime Number Subsequences

IF 17.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-01-31 DOI:10.29020/nybg.ejpam.v17i1.4979

Michael P. May

引用次数: 0

Abstract

We apply the Inclusion-Exclusion Principle to a unique pair of prime number subsequences to determine whether these subsequences form a small set or a large set and thus whether the infinite sum of the inverse of their terms converges or diverges. In this paper, we analyze the complementary prime number subsequences P′ and P′′ as well as revisit the twin prime subsequence P2.

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包含-排除原则在质数后序中的应用

我们将包含-排除原理应用于一对独特的质数子序列，以确定这些子序列是形成一个小集还是一个大集，从而确定它们的项逆的无限和是收敛还是发散。本文分析了互补质数子序列 P′和 P′′，并重新探讨了孪生质数子序列 P2。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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