The Logarithmic Prime Phase Law and the Geometry of Prime Distributions

Research manuscript on the Logarithmic Prime Phase Law (LPPL). Primes are mapped via p→e^{i log p} to the unit circle; we study the cumulative phase Θ(X). The paper introduces notation and constants (incl. Γ_p), reports numerical evidence, and outlines a reproducible analysis procedure—towards a geometric law of prime phases and a roadmap for further work.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-10-02
DOI
https://doi.org/10.5281/zenodo.17249390
Primary Topic
Bacterial Genetics and Biotechnology
Type
article
Field-Weighted Citation Impact
0.00
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article

The Logarithmic Prime Phase Law and the Geometry of Prime Distributions

Zenodo (CERN European Organization for Nuclear Research)
Bacterial Genetics and Biotechnology
article

The Logarithmic Prime Phase Law and the Geometry of Prime Distributions

article en

Abstract

Research manuscript on the Logarithmic Prime Phase Law (LPPL). Primes are mapped via p→e^{i log p} to the unit circle; we study the cumulative phase Θ(X). The paper introduces notation and constants (incl. Γ_p), reports numerical evidence, and outlines a reproducible analysis procedure—towards a geometric law of prime phases and a roadmap for further work.

Zenodo (CERN European Organization for Nuclear Research)
Technical University of Cluj-Napoca (RO)
Peace, Justice and strong institutions
Openalex Percentile: Top 36%
Bacterial Genetics and Biotechnology
DOIOpen Access PDFOpenAlex
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The Logarithmic Prime Phase Law and the Geometry of Prime Distributions · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS