On the Extension of the Gaussian Moat Problem

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).