# On the Extension of the Gaussian Moat Problem

## TL;DR

This paper introduces an algorithm for prime searching in three-dimensional space, extends previous work on the Gaussian Moat problem, and explains why such extensions are not feasible beyond four dimensions.

## Contribution

It develops a new algorithm for prime searching in 3D and provides theoretical insights into the limitations of extending the Gaussian Moat problem to higher dimensions.

## Key findings

- Algorithm successfully searches for primes in D space.
- Demonstrates the irregular distribution of primes in higher dimensions.
- Shows impossibility of extending the Gaussian Moat problem beyond four dimensions.

## Abstract

In this paper, we have developed an algorithm for the prime searching in $\mathbb{R}^3$. This problem was proposed by M. Das [Arxiv,2019]. This paper is an extension of her work. As we know the distribution of primes will get more irregular as we are going to infinity and going to the higher dimensions. We have also shown that why it is not possible to extend the Gaussian Moat problem for the higher dimensions (more than four dimensional plane).