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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.

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