Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity

[Submitted on 5 Jul 2026 (v1), last revised 14 Jul 2026 (this version, v3)]

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Abstract: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.

Submission history

From: Vincent Granville [view email]
[v1] Sun, 5 Jul 2026 08:09:25 UTC (413 KB)
[v2] Tue, 7 Jul 2026 04:32:34 UTC (515 KB)
[v3] Tue, 14 Jul 2026 19:56:25 UTC (515 KB)