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Corrigenda to ``New primitive whose degree is a Mersenne exponent,' and some new primitive pentanomials
Authors:Toshihiro Kumada  Hannes Leeb  Yoshiharu Kurita  Makoto Matsumoto
Institution:Daiwa Institute of Research Ltd. 15-6 Fuyuki, Koto-ku, Tokyo 135-8460, Japan ; Institute of Statistics, University of Vienna, Universitaetsstr. 5, 1010 Vienna, \mbox{Austria} ; Nippon Electric Control Equipment Industries Association, 2-1-17 Hamamatsu-cho, Minato-ku, Tokyo 105-0013 Japan ; Division of Mathematics, Integrated Human Studies, Kyoto University, Kyoto 606-8501 Japan
Abstract:We report an error in our previous paper #!K1!#], where we announced that we listed all the primitive trinomials over $GF(2)$ of degree 859433, but there is a bug in the sieve. We missed the primitive trinomial $X^{859433}+X^{170340}+1$ and its reciprocal, as pointed out by Richard Brent et al. We also report some new primitive pentanomials.

Keywords:Irreducible polynomials  primitive polynomials  finite field  Mersenne exponent
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