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An Investigation into a Putative 16-adic Correlation in Goldbach Partitions
This record contains the complete set of materials for a computational number theory investigation into a hypothesized link between the Goldbach Conjecture and a simplified, 16-adic Collatz-like dynamical system. The research initially explored whether the density of Goldbach partitions for an even number n showed a statistically significant ...openaire +1 more source
A recursion relation for the number of Goldbach partitions of an even integer
Journal of Discrete Mathematical Sciences and CryptographyThe contour integral representation of the number of Goldbach partitions of an even integer, G(n), is extended to an integral with a support function that equals a linear combination of integers {G(m)}. A support function is found such that there is a nontrivial integral relation relating number of Goldbach partitions of n and m < n.
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This paper presents an expanded empirical analysis of Goldbach partition counts G₂(n) for even integers up to 1 000 000. Using a high-precision fast-Fourier convolution method, all unordered prime pairs (p,q) satisfying p+q=n were computed and examined for inter-even variations Δ(n)=G₂(n+2)−G₂(n).
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Understanding Goldbach Partitions Through Composite Patterns and the Primorial Calendar
This paper develops a structural and combinatorial interpretation of Goldbach partitions that complements the standard prime-based counting method g(N). Insteadof scanning for primes, the approach decomposes Goldbach’s function into three components: (1) potential residue-compatible pairs, (2) pairs eliminated (“blocked”) bycomposite occupancy in the ...openaire +1 more source
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
Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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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