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arXiv · 2404.05506

FastECPP over MPI

Andreas Enge
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Abstract

The FastECPP algorithm is currently the fastest approach to prove theprimality of general numbers, and has the additional benefit of creatingcertificates that can be checked independently and with a lower complexity.This article shows how by parallelising over a linear number of cores,its quartic time complexity becomes a cubic wallclock time complexity;and it presents the algorithmic choices of the FastECPP implementation inthe author's \cm\ software (https://www.multiprecision.org/cm/) which has been written with massive parallelisation over MPI in mind, and which has been used to establish a new primality record for the "repunit" $(10^{86453} - 1) / 9$.

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Andreas Enge. 2024-04-08. FastECPP over MPI. https://arxiv.org/abs/2404.05506

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