Triple Reflections- A Discourse on Twin Prime Conjecture, Pascal’s Triangle, and Euler’s e

Triple Reflections- A Discourse on Twin Prime Conjecture, Pascal’s Triangle, and Euler’s e

Kwesi Atta Sakyi

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Triple Reflections- A Discourse on Twin Prime Conjecture, Pascal’s Triangle, and Euler’s e

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Abstract

The twin prime conjecture has attracted a lot of attention worldwide. It is still an unresolved problem, even though the work of Yitang Zhang has partially resolved it. The author of this paper aims to contribute to the discourse by employing basic mathematics and logic to arrive at some conclusions on the topic, and also to help in breaking new grounds. The researcher used secondary data to build his arguments in an exploratory manner, relying on the existing literature. The paper traces the background of the problem, and points to some of the breakthroughs that were made in the past. The paper examines Pascal’s triangle and, it makes some revealing discoveries on the coefficients. The author also examines Euler’s E, and links it to Pascal’s triangle, and the twin prime problem. Furthermore the author derives new arithmetic terms that he can use to produce infinite numbers of twin primes. The author also discusses how numbers so obtained can thoroughly be checked to be non-composite, thus extending the field of twin primes. The author finally points to the application of twin primes in industry, academia, and other areas of practical knowledge.

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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

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How to Cite This Article

Kwesi Atta Sakyi. 2020. \u201cTriple Reflections- A Discourse on Twin Prime Conjecture, Pascal’s Triangle, and Euler’s e\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 20 (GJSFR Volume 20 Issue F2): .

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GJSFR Volume 20 Issue F2
Pg. 21- 34

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 35Q31

Submission ReceivedFebruary 2, 2020
Peer Review Double Blind
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Accepted March 3, 2020
Published March 16, 2020

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March 23, 2020

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