Spectral Duality: Exact Explicit Formula

Riemann Zero - Prime Generator - Spectral Duality

Based on the Sech² Kernel Repair & Parseval/Convolution Bridge 📄 Read the Paper (DOI)

Position T = ln(x) T = 0.0000

Prime Field 𝒫(T) 0.0000

Zero Field 𝓩(T) 0.0000

Engine Controls

Speed 0.05x

Zeros (N) 200

Bandwidth (H) 0.050

Mathematical Unification

𝒫(T) ≡ 𝓩(T)

Using exact Fourier-pair Gaussian kernels, the arithmetic sum of primes 𝒫(T) is strictly equal to the spectral sum of zeros 𝓩(T).

High correlation guarantees the zeros directly generate the prime locations.

𝒫(T) — Prime Field (Arithmetic)

𝓩(T) — Zero Field (Spectral)

Exact Prime Location

SCANNER

Discovered Primes