What question did this study set out to answer?

The aim is to explore the origin of prime numbers and offer a unified theory for their distribution and associated conjectures.

March 6, 2026Open Access

A Unified Structure Theory of Prime Numbers - Conceptual Framework and Fundamental Path

Key Points

The aim is to explore the origin of prime numbers and offer a unified theory for their distribution and associated conjectures.
Develop a conceptual framework combining matrix structure and numeral-system constraints.
Establish connections between prime distribution, the Goldbach conjecture, and the Riemann hypothesis.
Identify minimal primitive rules to express the core laws of primes.
Demonstrated that prime distribution follows intrinsic constraints.
Connected major problems like the Goldbach conjecture and Riemann hypothesis through a unified structure.
Proposed that complex mathematical issues can have simple and self-consistent solutions.

Abstract

This paper returns to the fundamental origin of arithmetic, revealing the intrinsic constraints of prime distribution by a unified underlying structure. By combining matrix structure and numeral-system constraints, it establishes a unified closed loop connecting prime distribution, the Goldbach conjecture, and the Riemann hypothesis. This work shows that the core laws of primes can be expressed by minimal primitive rules, and complex problems admit simple, self-consistent, and complete solutions within a unified framework.

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Liang Feng

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A Unified Structure Theory of Prime Numbers - Conceptual Framework and Fundamental Path

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