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Prime Gaps In The Gaussian Integers

Kyle Bradford, James Taylor, George Volz

Abstract

In this paper we create a definition for prime gaps in the Gaussian integers using a boxcar metric. From this we used numerical methods to derive an asymptotic upper bound for the gaps in this scenario, namely O(log^2|p_{n}|).

Prime Gaps In The Gaussian Integers

Abstract

In this paper we create a definition for prime gaps in the Gaussian integers using a boxcar metric. From this we used numerical methods to derive an asymptotic upper bound for the gaps in this scenario, namely O(log^2|p_{n}|).

Paper Structure

This paper contains 5 sections, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Coding
  4. Results
  5. Appendix

Figures (1)

  • Figure 1: X represents the magnitude of the largest prime on the boundary of the gap, and gaps represents the magnitude of the gap