The Goldbach–Spiral Conjecture скачать в хорошем качестве

The Goldbach–Spiral Conjecture

We present a unification of two distinct approaches to prime number structure: Goldbach's ternary conjecture (1742), which asserts that every integer greater than 2 is the sum of three prime numbers, and the Spiral Prime Method (Cattell, 2025), a geometric framework that encodes primes as circles along a logarithmic spiral and uses center-to-center distance measurements to predict prime gaps. We demonstrate that the Goldbach triplet decompositions of an integer N induce a natural set of triangular arcs on the spiral diagram, and that the geometric centroids of these triangles exhibit a measurable proximity to the predicted position of the next prime. Validation across integers from 6 to 60 reveals that Goldbach arc centroids correlate with Spiral Method predictions at a rate consistent with the 92.9% gap prediction accuracy previously established. We further propose the Goldbach–Spiral Conjecture: that the density of ternary Goldbach representations of N is geometrically encoded in the spiral's red-line distance structure, and that this density function predicts the magnitude of the next prime gap.