A primitive trinomial of degree 6972593

214. R. P. Brent, S. Larvala and P. Zimmermann, A primitive trinomial of degree 6972593, Mathematics of Computation, 74 (2005), 1001-1002. Electronic version posted 25 May 2004.

Extended version: Research Report, INRIA Lorraine, Villers-lès-Nancy, France, 2005, to appear.

Preprint: dvi (6K), pdf (82K), ps (40K).

Extended version: dvi (10K), pdf (149K), ps (51K).


We describe a search for primitive trinomials of degree 6972593 over GF(2). The only primitive trinomials found were

x6972593 + x3037958 + 1 .

and its reciprocal. This completes the search for primitive trinomials whose degree is a Mersenne exponent less than ten million.


This extends the computation of [199]. For further results, see [230].

The search for degree 6972593 was performed on an average of about 300 processors and took approximately 230,000 Mips-years. The computation was started on 6 February 2001 and completed on 25 July 2003.

The primitive trinomial of degree 6972593 was found on 31 August 2002. The announcement is here, or see the September 2002 archives of the Number Theory List (NBMBTHRY) for a version with links.

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