Primality tests for Fermat numbers and 2^(2k+1)±2^(k+1)+1

2009/12/10 by Yu Tsumura, Tsumura, Yu
Computer Science · Mathematics · #11Y11 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11Y11

paper · pdf · doi:10.48550/arxiv.0912.2116

11 pages

arxiv created 2009/12/10 · openalex publication_date 2009/12/10 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Robert Denomme and Gordan Savin made a primality test for Fermat numbers 2^(2^k)+1 using elliptic curves. We propose another primality test using elliptic curves for Fermat numbers and also give primality tests for integers of the form 2^(2k+1)±2^(k+1)+1.

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