AI 中文总结
提出新方法攻克吉尔布雷斯质数猜想，基于筛分法给出新途径、成果及证明，介绍反向筛分概念并涉多领域应用。
AI 中文摘要
我提出一种新方法来攻克关于质数的引人入胜的吉尔布雷斯猜想，该猜想于1878年首次提出，至今未解决。问题表述简单，但数十年研究几乎无进展。本文通过基于筛分的新方法、新结果及证明、解决路径和参考文献改变局面，还介绍反向筛分概念及其在多领域的应用。
英文摘要
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.
