关于高斯护城河问题的推广
数论
2024-09-09 v2
摘要
本文中，我们发展了一种在 中搜索素数的算法。该问题由 M. Das [Arxiv,2019] 提出。本文是对其工作的推广。众所周知，素数的分布随着趋于无穷以及维数升高会变得更加不规则。我们还说明了为何无法将高斯护城河问题推广到更高维度（超过四维平面）。
引用
@article{arxiv.1901.10016,
title = {On the Extension of the Gaussian Moat Problem},
author = {Madhuparna Das},
journal= {arXiv preprint arXiv:1901.10016},
year = {2024}
}
备注
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