| viXra.org > Number Theory > viXra:2509.0033 |
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| viXra.org > Number Theory > viXra:2509.0033 |
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Number Theory |
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Authors: Rayan Bhuttoo
We demonstrate that prime numbers are precisely the indecomposable elements under a novel group operation defined on a circle, providing a geometric characterization of primality.By projecting integers onto a circle via the mapping θn = arccos(n/R), we show thatprimes exhibit intense clustering at the endpoints of the diameter, while composite numbers distribute uniformly. We formalize this observation by defining an angular density function F (n) that vanishes if and only if n is prime, with a rigorous proof based on the PrimeNumber Theorem. Furthermore, we analyze the Fourier spectrum of the prime distribution,revealing a distinct high-frequency signature. Finally, we conjecture connections betweenthis harmonic signature and the nontrivial zeros of the Riemann zeta function, suggesting anew approach to understanding prime distribution through geometric and harmonic analysis.
Comments: 7 Pages. License: CC BY-NC-ND 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
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[v1] 2025-09-05 16:30:58
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