# American Institute of Mathematical Sciences

November  2014, 8(4): 427-436. doi: 10.3934/amc.2014.8.427

## Some remarks on primality proving and elliptic curves

 1 Department of Mathematics, University of California, Irvine, Irvine, CA 92697-3875, United States

Received  January 2014 Published  November 2014

We give an overview of a method for using elliptic curves with complex multiplication to give efficient deterministic polynomial time primality tests for the integers in sequences of a special form. This technique has been used to find the largest proven primes $N$ for which there was no known significant partial factorization of $N-1$ or $N+1$.
Citation: Alice Silverberg. Some remarks on primality proving and elliptic curves. Advances in Mathematics of Communications, 2014, 8 (4) : 427-436. doi: 10.3934/amc.2014.8.427
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