Ten New Primitive Binary Trinomials

233. Richard P. Brent and Paul Zimmermann, Ten new primitive binary trinomials, Mathematics of Computation 78 (2009), 1197-1199. MR2476580 (2010a:11040).

Preprint: pdf (136K).


We exhibit ten new primitive trinomials over GF(2) of record degrees 24036583, 25964951, 30402457, and 32582657. This completes the search for the currently known Mersenne prime exponents.


For details of the computation, see the trinomial page.

For software, see the gf2x package.

For related papers, see [230, 232, 235].


Since the above was written, the GIMPS project found three more Mersenne primes! One of these is ruled out by Swan's theorem, but the others give the possibility of finding primitive trinomials of degree 42643801 and 43112609. For details, see the trinomial page.

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