The Icosahedral Structure of Prime Distribution

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Authors: Clifford Keeble
Cited by: 16
References: 3

Abstract

We show that the prime wheel modulus 66 derives from icosahedral geometry: 66 = D! × (V − 1) where D = 3 and V = 12. The values D = 3 and V = 12 are not arbitrary but geometrically forced: the Borwein integrals establish D = 3 as the unique closure dimension where D(D+1) = 2×D!, and the kissing number k(3) = 12 = V follows from sphere packing (Keeble, 2026). The 20 wheel slots equal φ(66) = F (icosahedron faces) and partition exactly 10/10 into quadratic residues (QR) and quadratic nonresidues (QNR) mod 11. This partition is encoded in the Gauss sum g = i√11, connecting prime distribution to roots of unity. We link this to Klein's 1884 work showing A₅ (icosahedral rotations) solves the quintic equation.

Fields of Study & Subjects

Analytic Number Theory Research Advanced Mathematical Identities Limits and Structures in Graph Theory

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
17 January 2026
Document type
Preprint