,周期性和初级性的概率
1Alternative Natural Philosophy Association, Bury St Edmunds IP30 9QX, UK.
Entropy (Basel, Switzerland)
|December 24, 2025
概括
这项研究揭示了周期数是复合的,并引入了新的度对初等性的测量. 这一发现加深了我们对素数分布及其与的联系的理解.
科学领域:
- 数学理论 数学理论
- 计算数学 计算数学 计算数学
- 信息理论 信息理论
背景情况:
- 原数的分布表现出有序性和随机性的特征.
- 了解素数的基本结构对于各种数学和计算领域至关重要.
研究的目的:
- 用二进制衍生框架研究,周期性和初级性之间的关系.
- 引入一种新的度测量方法来确定初级性.
- 探索这些发现对数论和密码学的含义.
主要方法:
- 使用二进制导数的计算框架.
- 证明与二进制周期性相关的质数和复合数行为的定理.
- 引入一个尺度不变的初级度的度度量,p ((s').
主要成果:
- 周期数被证明是复合的,只有一个微不足道的例外.
- 引入了一种新型的度量,p(s'),根据二进制结构提供了精确的初等概率.
- 结果显示,p{\displaystyle p{\text{s}}) 是二次的,统计学上是正确的,并且与二进制失序相关.
- 经验分析表明,质密度的方差很小,是双常态的,受中央极限定理的约束.
结论:
- 和素数的随机性之间存在着深厚的联系.
- 这些发现为数论的结构提供了新的见解.
- 对里曼假设,特殊素数类和加密应用的潜在影响.
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