A primitive trinomial of degree 6972593

A primitive trinomial of degree 6972593
HTML articles powered by AMS MathViewer

by Richard P. Brent, Samuli Larvala and Paul Zimmermann PDF

Math. Comp. 74 (2005), 1001-1002 Request permission

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

References

R. P. Brent, Search for primitive trinomials, http://www.comlab.ox.ac.uk/oucl/work/richard.brent/trinom.html.
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.
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.
Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, and Makoto Matsumoto, New primitive $t$-nomials $(t=3,5)$ over $\rm GF(2)$ whose degree is a Mersenne exponent, Math. Comp. 69 (2000), no. 230, 811–814. MR 1665959, DOI 10.1090/S0025-5718-99-01168-0
Thomas R. Nicely, Enumeration to $10^{14}$ of the twin primes and Brun’s constant, Virginia J. Sci. 46 (1995), no. 3, 195–204. MR 1401560
V. Shoup, NTL: A library for doing number theory (version 5.3.1), http://www.shoup.net/ntl/.
G. Woltman et al., GIMPS, The Great Internet Mersenne Prime Search, http://www.mersenne.org/.