Results 1 to 10 of about 131 (95)
Vectorizing and distributing number‐theoretic transform to count Goldbach partitions on Arm‐based supercomputers [PDF]
Concurrency Computation Practice and Experience, 2023 SummaryIn this article, we explore the usage of scalable vector extension (SVE) to vectorize number‐theoretic transforms (NTTs). In particular, we show that 64‐bit modular arithmetic operations, including modular multiplication, can be efficiently implemented with SVE instructions.
Ricardo Jesus +2 more
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Goldbach partitions and norms of cusp forms
Journal of Numerical Analysis and Approximation Theory, 2019 An integral formula for the Goldbach partitions requires uniform convergence of a complex exponential sum. The dependence of the coefficients of the series is found to be bounded by that of cusp forms.
Simon Brian Davis
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Computing the Number of Goldbach Partitions up to 5 108
Lecture Notes in Computer Science, 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.
Jörg Richstein
exaly +3 more sources
An FPGA systolic array using pseudo-random bit generators for computing Goldbach partitions
The Integration VLSI Journal, 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.
Dominique Lavenier
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On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 The Goldbach partitions of an even number, given by the sums of two prime addends, form the nonempty set for all integers 2n with 2≤n≤2×1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the
Simon Davis
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Computing Goldbach partitions using pseudo-random bit generator operators on an FPGA systolic array
Lecture Notes in Computer Science, 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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A Note on Goldbach Partitions of Large Even Integers [PDF]
The Electronic Journal of Combinatorics, 2015 Let $\Sigma_{2n}$ be the set of all partitions of the even integers from the interval $(4,2n], n>2,$ into two odd prime parts. We show that $|\Sigma_{2n}| \sim 2n^2/\log^2{n}$ as $n\to\infty$. We also assume that a partition is selected uniformly at random from the set $\Sigma_{2n}$. Let $2X_n\in (4,2n]$ be the size of this partition.
Ljuben Mutafchiev
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On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer [PDF]
Electronic Notes in Discrete Mathematics, 2016 Let $\mathcal{P}=\{p_1,p_2,...\}$ be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer $2k>4$ is a way of writing it as a sum of two primes from $\mathcal{P}$ without regard to order. Let $Q(2k)$ be the number of all Goldbach partitions of the number $2k$.
Ljuben Mutafchiev
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Goldbach Approach. A possible formula for calculating binary prime partitions of even numbers.
, 2022 Goldbach conjecture is one of the most famous open problems of mathematics, but its fame is justified by the time that this problem has been unproven and the long list of people who contribute one more piece to this puzzle, which is why this conjecture has two problems, the obvious level of difficulty, and the second is to be able to separate from all ...
Acuña T, Eduardo J.
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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 ...
Jie Pan
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