## 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).

## Abstract

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.

## Comments

For details of the computation, see the
trinomial page.
For software, see the gf2x
package.

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

## Postscript

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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