Toroidal Convergence of the Prime Vase: Gaussian Curvature of the Prime Number Surface and its Asymptotic Equivalence to a Toroid of Diverging Major Radius
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| Format: | Recurso digital |
| Language: | En |
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Zenodo
2026
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| _version_ | 1866901723336933376 |
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| author | Lainé, Jean-Pierre |
| author_facet | Lainé, Jean-Pierre |
| contents | <p>We compute the Gaussian curvature K(p_k) of the Prime Vase surface and demonstrate its asymptotic equivalence to a toroid of major radius R = p_k and minor radius rho = C_inf * ln(p_k). The normalized product K(p_k) * p_k * ln(p_k) converges to a finite constant, and the ratio K_vase/K_torus converges to 1. The main result is K(p_k) ~ 1/[p_k * C_inf * ln(p_k)] as k tends to infinity. Interactive visualizations are available at genesis1.net. Companion to: The Prime Vase, DOI: 10.5281/zenodo.19072444. Part of the Genesis-1 research program.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19073278 |
| institution | Zenodo |
| language | enc |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Toroidal Convergence of the Prime Vase: Gaussian Curvature of the Prime Number Surface and its Asymptotic Equivalence to a Toroid of Diverging Major Radius Lainé, Jean-Pierre prime numbers, Gaussian curvature, toroid, surface of revolution, prime number theorem, prime gaps, golden angle, Genesis-1, differential geometry, asymptotic analysis <p>We compute the Gaussian curvature K(p_k) of the Prime Vase surface and demonstrate its asymptotic equivalence to a toroid of major radius R = p_k and minor radius rho = C_inf * ln(p_k). The normalized product K(p_k) * p_k * ln(p_k) converges to a finite constant, and the ratio K_vase/K_torus converges to 1. The main result is K(p_k) ~ 1/[p_k * C_inf * ln(p_k)] as k tends to infinity. Interactive visualizations are available at genesis1.net. Companion to: The Prime Vase, DOI: 10.5281/zenodo.19072444. Part of the Genesis-1 research program.</p> |
| title | Toroidal Convergence of the Prime Vase: Gaussian Curvature of the Prime Number Surface and its Asymptotic Equivalence to a Toroid of Diverging Major Radius |
| topic | prime numbers, Gaussian curvature, toroid, surface of revolution, prime number theorem, prime gaps, golden angle, Genesis-1, differential geometry, asymptotic analysis |
| url | https://doi.org/10.5281/zenodo.19073278 |