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Mathematics of Computation

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Ten new primitive binary trinomials


Authors: Richard P. Brent and Paul Zimmermann
Journal: Math. Comp. 78 (2009), 1197-1199
MSC (2000): Primary 11B83, 11Y16; Secondary 11-04, 11T06, 11Y55, 12-04
DOI: https://doi.org/10.1090/S0025-5718-08-02170-4
Published electronically: August 1, 2008
MathSciNet review: 2476580
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Abstract | References | Similar Articles | Additional Information

Abstract: We exhibit ten new primitive trinomials over GF(2) of record degrees $ 24\,036\,583$, $ 25\,964\,951$, $ 30\,402\,457$, and $ 32\,582\,657$. This completes the search for the currently known Mersenne prime exponents.


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Additional Information

Richard P. Brent
Affiliation: Australian National University, Canberra, Australia
Email: trinomials@rpbrent.com

Paul Zimmermann
Affiliation: INRIA Nancy, Grand Est, Villers-lès-Nancy, France
Email: Paul.Zimmermann@loria.fr

DOI: https://doi.org/10.1090/S0025-5718-08-02170-4
Keywords: $ {GF}(2)[x]$, irreducible polynomials, irreducible trinomials, primitive polynomials, primitive trinomials, Mersenne exponents, Mersenne numbers
Received by editor(s): April 15, 2008
Published electronically: August 1, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.