Ten new primitive binary trinomials (original) (raw)

Article Dans Une Revue Mathematics of Computation Année : 2009

Résumé

We exhibit ten new primitive trinomials over GF(2)\GF(2)GF(2) of record degrees 24,036,58324\,036\,58324,036,583, 25,964,95125\,964\,95125,964,951, 30,402,45730\,402\,45730,402,457, and 32,582,65732\,582\,65732,582,657. This completes the search for the currently known Mersenne prime exponents.

Mots clés

• $GF(2)[x]$
• irreducible polynomials
• irreducible trinomials
• primitive polynomials
• primitive trinomials
• Mersenne exponents
• Mersenne numbers

Dates et versions

inria-00337525 , version 1 (07-11-2008)

Identifiants

• HAL Id : inria-00337525 , version 1

Citer

Richard P. Brent, Paul Zimmermann. Ten new primitive binary trinomials. Mathematics of Computation, 2009, 78 (266), pp.1197-1199. ⟨inria-00337525⟩

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