Results 61 to 70 of about 521 (101)

A Proof of Goldbach Conjecture by Using Goldbach Partition Model Table and Sieve Functions

2015
Goldbach's Conjecture(GC) states that any even integer ≥ 4 can be represented by the sum of two prime numbers. This was conjectured by Christian Goldbach in 1742 and still remains unproved. In this thesis we proved GC by introducing Goldbach Partition Model Table(GPMT) and Sieve Functions(SFs).
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An FPGA systolic array using pseudo-random bit generators for computing Goldbach partitions

Integration, 2000
Summary: A linear systolic array of 256 cells for computing the Goldbach partitions has been designed and implemented on the FPGA PeRLe-1 platform. Fast computation is achieved using a counter based on a pseudo-random bit generator. Beyond this application we show that FPGA technology tends to promote such applications.
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Computing the Number of Goldbach Partitions up to 5 108

2000
Computing the number of Goldbach partitions $$g(n) = \#\{(p,q) | n = p + q, p \leq ~q\}$$ of all even numbers n up to a given limit can be done by a very simple, but space-demanding sequential procedure. This work describes a distributed implementation for computing the number of partitions with minimal space requirements.
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Computing Goldbach partitions using pseudo-random bit generator operators on an FPGA systolic array

1998
Calculating the binary Goldbach partitions for the first 128× 106 numbers represents weeks of computation with the fastest microprocessors. This paper describes an FPGA systolic implementation for reducing the execution time. High clock frequency is achieved using operators based on pseudo-random bit generator.
Dominique Lavenier, Yannick Saouter
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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 ...
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A recursion relation for the number of Goldbach partitions of an even integer

Journal of Discrete Mathematical Sciences and Cryptography
The 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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Goldbach Gap Studies v2 — Empirical Variation of Goldbach Partition Counts up to 10⁶ (Unicode Math Edition)

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 ...
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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 ...
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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 ...
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