破解百年未解的素数猜想，揭示其在金融科技与安全中的新应用
Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity
- 提出基于筛法的新方法，引入反向筛法突破传统研究瓶颈
- 证明多个新结论并给出解题明确路径，首次系统化推进该猜想
- 成果可应用于随机性检测、欺诈识别、时间序列混沌分析等场景
本文提出一种新方法攻克素数领域著名难题——吉尔布雷斯猜想（1878年提出，至今未解）。问题本身简单易懂，但数十年来进展甚微。本研究通过筛法构建新理论框架，提出反向筛法概念，证明多项新结果并给出完整求解路径。研究还拓展至随机性测试、模式与欺诈检测、网络安全、合成数据生成、序列分类归一化等领域，并发现时间序列中一类新型混沌现象，包括布朗运动。文中探讨了神秘素数、禁止的素数构型、细胞自动机及等价序列类约化等创新方向。
原文摘要 · Abstract (English)
I propose a new methodology to attack the fascinating Gilbreath's conjecture about prime numbers, first posted in 1878 and unsolved to this day. The problem statement is rudimentary: kids can understand it. However, despite decades of research, almost no progress has been made. This paper changes the game by presenting a new approach based on sieving, a number of new results with proof, a precise path to the solution, and solid references. It also introduces the concept of reverse sieving, along with applications to testing randomness, pattern and fraud detection, cybersecurity, synthetic data, sequence categorization and normalization, or to detect and quantify a new type of chaos in time series including Brownian motions. Magic primes, forbidden prime number constellations, cellular automata, and reduction via classes of equivalent sequences, are some of the innovative and promising topics discussed in the paper.
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