Dreibens Modulo 7: A New Formula for Primality Testing

Authors

  • Arthur Diep-Nguyen Boston College

DOI:

https://doi.org/10.6017/eurj.v12i1.9303

Keywords:

Mathematics, Dreibens, Prime Number Theory

Abstract

In this paper, we discuss strings of 3’s and 7’s, hereby dubbed “dreibens.” As a first step towards determining whether the set of prime dreibens is infinite, we examine the properties of dreibens when divided by 7. by determining the divisibility of a dreiben by 7, we can rule out some composite dreibens in the search for prime dreibens. We are concerned with the number of dreibens of length n that leave a remainder i when divided by 7. By using number theory, linear algebra, and abstract algebra, we arrive at a formula that tells us how many dreibens of length n are divisible by 7. We also find a way to determine the number of dreibens of length n that leave a remainder i when divided by 7. Further investigation from a combinatorial perspective provides additional insight into the properties of dreibens when divided by 7. Overall, this paper helps characterize dreibens, opens up more paths of inquiry into the nature of dreibens, and rules out some composite dreibens from a prime dreiben search.

Author Biography

Arthur Diep-Nguyen, Boston College

ARTHUR DIEP-NGUYEN is a sophomore at Boston College from San Marino, California. While originally a Biology major, Arthur discovered a passion for mathematics during the fall semester of his freshman year, when his Calculus II professor Igor Minevich introduced him to various proofs, puzzles, and other topics in math. This initial experience spurred Arthur to expand his academic horizons. Since then, Arthur has worked on math research with classmates and continues to pursue his interests in both science and math. Currently a Biochemistry and Mathematics double major, Arthur is also a trombonist in the University Wind Ensemble and in the bOp! Jazz Ensemble.

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Published

2016-04-22

How to Cite

Diep-Nguyen, A. (2016). Dreibens Modulo 7: A New Formula for Primality Testing. Elements, 12(1). https://doi.org/10.6017/eurj.v12i1.9303

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Section

Articles