New primitive $t$-nomials $(t = 3,5)$ over $GF(2)$ whose degree is a Mersenne exponent

Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, Makoto Matsumoto
1999 Mathematics of Computation  
All primitive trinomials over GF (2) with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are X 859433 + X 288477 + 1 and its reciprocal. Also two examples of primitive pentanomials over GF (2) with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.
doi:10.1090/s0025-5718-99-01168-0 fatcat:wwjv24trzbblpgs2r5vnl4d4dy