Primality tests for 2^kn-1 using elliptic curves
Number Theory
2009-12-31 v1
Abstract
We propose some primality tests for 2^kn-1, where k, n in Z, k>= 2 and n odd. There are several tests depending on how big n is. These tests are proved using properties of elliptic curves. Essentially, the new primality tests are the elliptic curve version of the Lucas-Lehmer-Riesel primality test. Note:An anonymous referee suggested that Benedict H. Gross already proved the same result about a primality test for Mersenne primes using elliptic curve.
Keywords
Cite
@article{arxiv.0912.5279,
title = {Primality tests for 2^kn-1 using elliptic curves},
author = {Yu Tsumura},
journal= {arXiv preprint arXiv:0912.5279},
year = {2009}
}
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8 pages