The Great Trinomial Hunt
235. Richard P. Brent and
The great trinomial hunt,
Notices of the American Mathematical Society 58, 2 (2011), 233-239.
We describe a search for primitive trinomials of high degree
and its interaction with the Great Internet Mersenne prime search
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
See also the trinomial page.
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