English

On the Extension of the Gaussian Moat Problem

Number Theory 2024-09-09 v2

Abstract

In this paper, we have developed an algorithm for the prime searching in R3\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).

Keywords

Cite

@article{arxiv.1901.10016,
  title  = {On the Extension of the Gaussian Moat Problem},
  author = {Madhuparna Das},
  journal= {arXiv preprint arXiv:1901.10016},
  year   = {2024}
}

Comments

The proofs of Theorem 1 and 2 are incorrect. In the proof of Thm 1, proving the infinitude of primes (of special forms) is more complex. The given argument here uses incorrect elementary methods. The infinitude of natural prime numbers doesn't prove the infinitude of three-dimensional primes. It is the same as saying that the infinitude of primes implies the infinitude of twin primes