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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A primitive trinomial of degree 6972593


Authors: Richard P. Brent, Samuli Larvala and Paul Zimmermann
Journal: Math. Comp. 74 (2005), 1001-1002
MSC (2000): Primary 11B83; Secondary 11-04, 11N35, 11R09, 11T06, 11Y55, 12-04
Published electronically: May 25, 2004
MathSciNet review: 2114660
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Abstract | References | Similar Articles | Additional Information

Abstract: The only primitive trinomials of degree $6972593$ over $\operatorname{GF}(2)$are $x^{6972593} + x^{3037958} + 1$ and its reciprocal.


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Additional Information

Richard P. Brent
Affiliation: Oxford University Computing Laboratory, Oxford OX1 3QD, United Kingdom
Email: trinomials@rpbrent.co.uk

Samuli Larvala
Affiliation: Helsinki University of Technology, Espoo, Finland
Email: slarvala@cc.hut.fi

Paul Zimmermann
Affiliation: LORIA/INRIA Lorraine, 615 rue du jardin botanique, BP 101, F-54602 Villers-lès-Nancy, France
Email: Paul.Zimmermann@loria.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01673-4
PII: S 0025-5718(04)01673-4
Keywords: Irreducible trinomials, primitive trinomials, Mersenne numbers
Received by editor(s): August 26, 2003
Received by editor(s) in revised form: October 6, 2003
Published electronically: May 25, 2004
Article copyright: © Copyright 2004 American Mathematical Society