Prime Gaps In The Gaussian Integers

TL;DR

This paper defines prime gaps in Gaussian integers using a boxcar metric and derives an asymptotic upper bound of O(log^2|p_{n}|) through numerical methods.

Contribution

It introduces a novel definition of prime gaps in Gaussian integers and establishes an asymptotic upper bound for these gaps.

Findings

Derived an asymptotic upper bound of O(log^2|p_{n}|) for prime gaps in Gaussian integers.

Used numerical methods to analyze prime gaps in the Gaussian integers.

Provided a new framework for understanding prime distribution in complex quadratic integer rings.

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}|).