Primality tests for 2^kn-1 using elliptic curves

2009/12/29 by Yu Tsumura, Tsumura, Yu
Mathematics · #11Y05 #11Y11 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11Y05 #msc:11Y11

paper · pdf · doi:10.48550/arxiv.0912.5279

8 pages

arxiv created 2009/12/29 · arxiv updated 2010/01/14

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.

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