Results 91 to 100 of about 557,668 (129)

Deep learning-based approximation of Goldbach partition function

Discrete Mathematics, Algorithms and Applications, 2021
Goldbach’s conjecture is one of the oldest and famous unproved problems in number theory. Using a deep learning model, we obtain an approximation of the Goldbach partition function, which counts the number of ways of representing an even number greater than 4 as a sum of two primes.
Eunmi Kim
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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.
S. Davis
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Goldbach partitions and sequences

Resonance, 2014
Properties of Goldbach partitions of numbers, as sums of primes, are presented and their potential applications to cryptography are described. The sequence of the number of partitions has excellent randomness properties. Goldbach partitions can be used to create ellipses and circles on the number line and they can also be harnessed for cryptographic ...
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On the sum of partition norms and its connection to norms of partitions with parts greater than one

Notes on Number Theory and Discrete Mathematics
We study the partition norm—the product of the parts of a partition—with emphasis on partitions whose parts all exceed 1. We obtain two bivariate recurrences for the sum of norms over partitions into distinct parts, including a refinement that separates ...
M. Rana, Harman Kaur, Abhimanyu Kumar
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Structural Failure Mode Analysis of the Binary Goldbach Conjecture

Mathematics and Computer Science
This paper analyzes the Binary Goldbach Conjecture (bGC) through a deterministic structural lens, employing a Failure Mode Analysis (FMA) framework to map prime and composite inventories onto the Left-Right Partition Table (LRPT).
Ioannis Papadakis
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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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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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Analytic study of norms of prime partitions

, 2021
Abhimanyu Kumar
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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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Phenomenological Evidence of GUE Statistics and Thermodynamic Stability in Goldbach Partitions

This preprint presents a computational and phenomenological analysis of Goldbach's Conjecture through the combined lenses of spectral theory (GUE random matrix statistics) and statistical mechanics (thermodynamic entropy). Using an integral-refined Hardy–Littlewood heuristic with explicit Singular Series computation, we achieve convergence ratios of ≈1.
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