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The Goldbach Quasicrystal: Topological Protection and Scale-Invariance in Prime Partition Networks
This preprint presents a novel network-theoretic approach to the Goldbach Conjecture through computational analysis of the "Goldbach Graph" - a network where even integers are nodes connected by shared prime components in their partitions. We analyze networks scaling from N=6,000 to N=1,000,000, revealing three key structural signatures: (1) Phase ...openaire +1 more source
Spectral Mechanics of the Goldbach Partition: A Probabilistic Criterion for Twin Primes
We establish a theoretical link between the complex zeros of Goldbach partition polynomials and the asymptotic density of twin primes. Starting from Yamagishi's identity, which expresses the twin prime counting function $\pi_{2}(n)$ in terms of minimal Goldbach primes, we derive a spectral observable $\delta(n)$ corresponding to the gap between ...openaire +1 more source
Empirical Verification of the Modular Law in Goldbach Partitions up to 300000
1️⃣ Zenodo Description – PDF (Article) For file: Empirical Verification of the 2:1:1 Modular Law in Goldbach Partitions up to 300000.pdf(you can shorten the file name on Zenodo if you like) Description This article presents a detailed empirical study of the modular structure of Goldbach partitions up to 2n=300,0002n = 300{,}0002n=300,000. For eachopenaire +1 more source
An Exact Identity for the Twin Prime Counting Function Derived from Minimal Goldbach Partitions
Assuming the Goldbach conjecture, we establish a quantitative connection between the twin prime counting function $\pi_2(x)$ and the distribution of minimal primes in Goldbach decompositions of even integers. For each even integer $k \geq 4$, define $p(k)$ as the smallest prime $p$ such that $k - p$ is also prime.openaire +1 more source
Study of Structured Primes in Goldbach Partitions
Annual International Conference on Computational Mathematics, Computational Geometry & Statistics (CMCGS 2012), 2012openaire +1 more source
ALGEBRAIC AND GEOMETRIC REPRESENTATION OF GOLDBACH PARTITIONS IN THE COMPLEX PLANE
openaire +1 more sourceA Generalization of the Quantitative Link Between Twin Primes and Minimal Goldbach Partitions
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