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整数分区可以检测到素数.

William Craig1, Jan-Willem van Ittersum1, Ken Ono2

  • 1Department of Mathematics, United States Naval Academy, Annapolis, MD 21402.

Proceedings of the National Academy of Sciences of the United States of America
|September 20, 2024
PubMed
概括
此摘要是机器生成的。

整数分区出乎意料地识别了素数. 涉及麦克马洪的特定方程.

关键词:
分隔板是指隔墙,分隔板是指隔墙.素数是什么意思 素数是什么意思准模块化形式的形式.

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科学领域:

  • 数学理论 数学理论
  • 添加数理论 添加数理论
  • 组合学是一种组合学.

背景情况:

  • 整数分区是加法数论中的基本对象,表示正整数作为正整数的和.
  • 麦克马洪的分区函数是经过充分研究的组合函数工具,在各种数学领域都有应用.
  • 识别素数是数论中的一个核心问题,对密码学和计算数学有重大影响.

研究的目的:

  • 调查整数分区与素数识别之间的关系.
  • 为了回答施耐德关于在检测素数时使用分区函数的问题.
  • 使用麦克马洪的分区函数建立新的质量检测方程.

主要方法:

  • 利用整数分区的属性和麦克马洪分区函数.
  • 开发和分析涉及这些分区函数的特定数学方程.
  • 证明这些方程的解与整数的初等性之间的等价性.

主要成果:

  • 证明整数分区可以通过特定方程检测素数.
  • 给出一个素数检测方程的例子:一个整数n ≥2是素数,如果,只有如果[公式:参见文本].
  • 证明了无限多的原始检测方程的存在,这些方程对MacMahonesque分区函数具有恒定系数.

结论:

  • 在整数分区和质数识别之间建立了一个新的和意想不到的联系.
  • 这些发现为理解和检测素数提供了新的工具.
  • 这项研究为增加数论和组合论的进一步探索开辟了道路.