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arXiv · 1404.0107

A framework for deterministic primality proving using elliptic curves with complex multiplication

Alexander Abatzoglou·Alice Silverberg·Andrew V. Sutherland·Angela Wong
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Abstract

We provide a framework for using elliptic curves with complex multiplication to determine the primality or compositeness of integers that lie in special sequences, in deterministic quasi-quadratic time. We use this to find large primes, including the largest prime currently known whose primality cannot feasibly be proved using classical methods.

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Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland, Angela Wong. 2014-10-11. A framework for deterministic primality proving using elliptic curves with complex multiplication. https://doi.org/10.1090/mcom%2F3001

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