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


Authors: Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland and Angela Wong
Journal: Math. Comp. 85 (2016), 1461-1483
MSC (2010): Primary 11Y11; Secondary 11G05, 14K22, 11A51
DOI: https://doi.org/10.1090/mcom/3001
Published electronically: July 20, 2015
MathSciNet review: 3454371
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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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Additional Information

Alexander Abatzoglou
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: aabatzog@math.uci.edu

Alice Silverberg
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: asilverb@math.uci.edu

Andrew V. Sutherland
Affiliation: Department of Mathematics, MIT, Cambridge, Massachusetts 02139
Email: drew@math.mit.edu

Angela Wong
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: awong@math.uci.edu

DOI: https://doi.org/10.1090/mcom/3001
Received by editor(s): March 31, 2014
Received by editor(s) in revised form: October 11, 2014
Published electronically: July 20, 2015
Additional Notes: This work was supported by the National Science Foundation under grants CNS-0831004 and DMS-1115455.
Article copyright: © Copyright 2015 American Mathematical Society