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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.doi:10.1090/s0025-5718-99-01168-0 fatcat:wwjv24trzbblpgs2r5vnl4d4dy