Twelve new primitive binary trinomials

2016/05/23 by Richard P. Brent, Paul Zimmermann, Brent, Richard P. +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Coding theory and cryptography #math.NT #msc:11-04 #msc:11B83 #msc:11N35 #msc:11R09 #msc:11T06 #msc:11Y16 #msc:11Y55 #msc:12-04

paper · pdf · doi:10.48550/arxiv.1605.09213

2 pages, 1 table

arxiv created 2016/05/24 · arxiv updated 2016/05/31

Abstract

We exhibit twelve new primitive trinomials over GF(2) of record degrees 42643801, 43112609, and 74207281. In addition we report the first Mersenne exponent not ruled out by Swan's theorem - namely 57885161 - for which no primitive trinomial exists. This completes the search for the currently known Mersenne prime exponents.

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