MillenniumChecked

Overview

The Millennium Prize Problems are seven of the deepest open questions in mathematics. Each has resisted resolution for decades, approached through methods native to its own domain — analytic number theory, topology, fluid dynamics, complexity theory.

This project does not claim to solve them. It asks a different question: what if these problems share a common structural language that the tools of each individual domain cannot see?

The framework developed here — built from prime number elimination cycles, harmonic interference, and relational arithmetic — offers a way to restate each problem in terms of the same underlying mechanisms. Whether this restatement brings resolution closer is an open question. What it offers is a different angle of observation.

The foundation is the Four Pillars of Prime Number Order: a constructive model in which primes arise not as atoms of multiplication, but as survivors of a deterministic elimination process — and in which the harmonic structure of that process connects naturally to questions about zeros, gaps, energy, and complexity.

This is a working research program, not a collection of finished proofs. Formal papers and preprints are available on Zenodo. The status of each problem page reflects the current depth of the structural analysis.

Structure of the Problems

      ┌───── Birch and Swinnerton-Dyer
      ├───── Riemann Hypothesis
      ├───── Hodge Conjecture
  ┌───┴─── approached via prime number structure
  │
  │   ┌───── P ≠ NP
  │   ├───── Yang–Mills Mass Gap
  │   ├───── Navier–Stokes
  │   ├───── Poincaré Conjecture
  ├───┴─── approached via constructive structural analysis
  │
──┴────────────────────────────────────────
   Four Pillars of Prime Number Order
   (Elimination, Density, Resonance, Wave)