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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

The Linear and Quadratic Nature of Sequences for Determining Prime Numbers by Elimination of Composites

Jonathan M. Dugas1 and Brian M. O’Connor1
  • 1 Tennessee Technological University, United States

Abstract

A previously derived set of sequences for generating prime numbers is modified by various algebraic and trigonometric manipulations. The modified sequences are then used to more efficiently generate prime numbers. The modified sequences are simplified from their original form and are much easier to implement into a computer program. It is shown by computation that the modified sequences more efficiently determine prime numbers because the modified sequences provide flexibility with their implementation. The added flexibility allows for the removal of redundancy in the overall process, which decreases the amount of data to process; thus, the efficiency of the prime number generator is significantly improved.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 119-128

DOI: https://doi.org/10.3844/jmssp.2018.119.128

Submitted On: 26 March 2018 Published On: 16 May 2018

How to Cite: Dugas, J. M. & O’Connor, B. M. (2018). The Linear and Quadratic Nature of Sequences for Determining Prime Numbers by Elimination of Composites. Journal of Mathematics and Statistics, 14(1), 119-128. https://doi.org/10.3844/jmssp.2018.119.128

Open AccessCopyright: © 2018 Jonathan M. Dugas and Brian M. O’Connor. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Primes
  • Sequences
  • Linear
  • Quadratic
  • Equations