| _version_ | 1866901341901684736 |
|---|---|
| author | Redwaan, Ezadiin |
| author_facet | Redwaan, Ezadiin |
| contents | <p>We present a universal, non-constructive proof of the Strong Goldbach<br>Conjecture and the Twin Prime Conjecture by shifting the problem<br>from arithmetic density to Geometrical Transformation. By<br>mapping the interaction between addition and multiplication onto a<br>prime-based vector space, we prove that the identity 2n cos(θ) = a+b<br>is a structural requirement of the space for every even integer 2n.<br>This formulation resolves the parity problem through the Dot<br>Product, demonstrating that a prime partition (a, b) is geometrically<br>necessitated by the scalar projection of prime-based vectors. Furthermore,<br>we show that the limiting behavior of the angular discrepancy<br>θ necessitates the infinite existence of Twin Primes. This research<br>establishes that prime distribution is a fundamental consequence of a<br>deeper geometric necessity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19358674 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Scalar Product Approach to Strong Goldbach Conjecture and Twin Primes Conjecture Redwaan, Ezadiin <p>We present a universal, non-constructive proof of the Strong Goldbach<br>Conjecture and the Twin Prime Conjecture by shifting the problem<br>from arithmetic density to Geometrical Transformation. By<br>mapping the interaction between addition and multiplication onto a<br>prime-based vector space, we prove that the identity 2n cos(θ) = a+b<br>is a structural requirement of the space for every even integer 2n.<br>This formulation resolves the parity problem through the Dot<br>Product, demonstrating that a prime partition (a, b) is geometrically<br>necessitated by the scalar projection of prime-based vectors. Furthermore,<br>we show that the limiting behavior of the angular discrepancy<br>θ necessitates the infinite existence of Twin Primes. This research<br>establishes that prime distribution is a fundamental consequence of a<br>deeper geometric necessity.</p> |
| title | A Scalar Product Approach to Strong Goldbach Conjecture and Twin Primes Conjecture |
| url | https://doi.org/10.5281/zenodo.19358674 |