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The Composite Density Law: A Deterministic Framework for Prime Gaps

23 March 2025, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

Prime gaps have been studied for centuries, yet their deterministic structure has remained elusive. In this paper, I introduce the Composite Density Law, which explains the formation of large prime gaps based on the density of composite numbers. This law provides a deterministic framework for understanding prime gap behavior, surpassing probabilistic models. Extensive computational validation up to 10^20 confirms its universal applicability, marking a significant advancement in number theory.

Keywords

Prime Gaps
Composite Density
Number Theory
Deterministic Models
Prime Number Theorem
Computational Mathematics

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Version History

Mar 23, 2025 Version 1

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The content is available under CC BY 4.0 [opens in a new tab]

DOI

10.33774/coe-2025-d41kt
D O I: 10.33774/coe-2025-d41kt [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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