The Great Trinomial Hunt

235. Richard P. Brent and Paul Zimmermann, The great trinomial hunt, Notices of the American Mathematical Society 58, 2 (2011), 233-239. arXiv:1005.1967v1

Preprint: pdf (184K).


We describe a search for primitive trinomials of high degree and its interaction with the Great Internet Mersenne prime search (GIMPS). The search is complete for trinomials whose degree is the exponent of a Mersenne prime, for all 47 currently known Mersenne primes.


A new Mersenne prime (the 48th in order of discovery, with exponent 57885161) was found by the GIMPS project on 25 January 2013. Although the exponent is 1 (mod 8) so primitive trinomials are not ruled out by Swan's theorem, we found (on 13 May 2013) that there are no primitive trinomials of degree 57885161 [joint work with Bill Hart, Alexander Kruppa and Paul Zimmermann].

For related papers, see [230, 232, 233].

See also the trinomial page.

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