Primes as a Field on a Discrete Torus

Key Points

• This research aims to analyze the distribution of prime numbers in relation to a discrete torus using modular embedding.
• Mapped prime numbers using modular embedding Phi_k(n) = (n mod p1, ..., n mod pk).
• Investigated prime distribution with the decomposition formula P(prime at s) = mu(s) · S(s) · rho(s).
• Empirical validation at N = 10^8.
• Identified a non-constant prime preference field with measurable Fourier structure.
• Validated conjectures regarding quasi-twin prime signature and prime spectral decomposition.
• Envelope curve V(m) was found to approximate C/ln(m).

Abstract