English

Twelve new primitive binary trinomials

Number Theory 2016-05-31 v1

Abstract

We exhibit twelve new primitive trinomials over GF(2) of record degrees 4264380142643801, 4311260943112609, and 7420728174207281. In addition we report the first Mersenne exponent not ruled out by Swan's theorem - namely 5788516157885161 - for which no primitive trinomial exists. This completes the search for the currently known Mersenne prime exponents.

Cite

@article{arxiv.1605.09213,
  title  = {Twelve new primitive binary trinomials},
  author = {Richard P. Brent and Paul Zimmermann},
  journal= {arXiv preprint arXiv:1605.09213},
  year   = {2016}
}

Comments

2 pages, 1 table

R2 v1 2026-06-22T14:12:49.810Z