3 results for “Jonathan M. Dugas”

Research ArticleOpen accessIn the author namesThe Linear and Quadratic Nature of Sequences for Determining Prime Numbers by Elimination of CompositesJonathan M. Dugas, Brian M. O’ConnorA 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 … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 16 May 2018 · 7,408 accessesView PDF Cite

HypothesisOpen accessIn the author namesSequences for Determination of Prime Numbers by Elimination of CompositesJonathan M. Dugas, Brian M. O’ConnorIn this study, sequences are used for direct computation of prime numbers. A single equation for generating all prime numbers with the exception of 2 and 3 and composite numbers that are not divisible by 2 or 3 is presented. A periodicity to the indices of the composites generated by that equation is determined. An equation to determine the indices … …Journal of Mathematics and Statistics, Vol. 13, Issue 3 · 20 Jul 2017 · 8,046 accessesView PDF Cite