Triple Reflections- A Discourse on Twin Prime Conjecture, Pascal's Triangle, and Euler's e (Global Journal of Science Frontier Research, 2020)
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.
Keywords: arithmetic progression; binomial expansion; brun; cryptology; eratosthenes