Remote Access Mathematics of Computation
Green Open Access

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)

  • 1. R. P. Brent, Search for primitive trinomials, http://www.comlab.ox.ac.uk/oucl/work/ richard.brent/trinom.html.
  • 2. R. P. Brent, S. Larvala and P. Zimmermann, A fast algorithm for testing reducibility of trinomials mod 2 and some new primitive trinomials of degree 3021377, Math. Comp. 72 (2003), 1443-1452.
  • 3. R. P. Brent and P. Zimmermann, Algorithms for finding almost irreducible and almost primitive trinomials, in Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams, Fields Institute, Toronto, 2004, to appear.
  • 4. T. Kumada, H. Leeb, Y. Kurita and M. Matsumoto, New primitive $t$-nomials $(t = 3$, $5)$ over $\operatorname{GF}(2)$whose degree is a Mersenne exponent, Math. Comp. 69 (2000), 811-814; Corrigenda: ibid 71 (2002), 1337-1338. MR 2000i:11183; MR 2003c:11153
  • 5. T. J. Nicely, Enumeration to $10^{14}$ of the twin primes and Brun's constant, Virginia Journal of Science 46 (1995), 195-204. MR 97e:11014
  • 6. V. Shoup, NTL: A library for doing number theory (version 5.3.1), http://www.shoup.net/ ntl/.
  • 7. G. Woltman et al., GIMPS, The Great Internet Mersenne Prime Search, http://www. mersenne.org/.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11B83, 11-04, 11N35, 11R09, 11T06, 11Y55, 12-04

Retrieve articles in all journals with MSC (2000): 11B83, 11-04, 11N35, 11R09, 11T06, 11Y55, 12-04


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
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