Ten new primitive binary trinomials

Richard P. Brent; Paul Zimmermann

doi:10.1090/S0025-5718-08-02170-4

Ten new primitive binary trinomials

Richard P. Brent, Paul Zimmermann

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We exhibit ten new primitive trinomials over GF(2) of record degrees 24036 583, 25 964951, 30402 457, and 32 582 657. This completes the search for the currently known Mersenne prime exponents.

Original language	English
Pages (from-to)	1197-1199
Number of pages	3
Journal	Mathematics of Computation
Volume	78
Issue number	266
DOIs	https://doi.org/10.1090/S0025-5718-08-02170-4
Publication status	Published - 2009

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title = "Ten new primitive binary trinomials",

abstract = "We exhibit ten new primitive trinomials over GF(2) of record degrees 24036 583, 25 964951, 30402 457, and 32 582 657. This completes the search for the currently known Mersenne prime exponents.",

keywords = "GF(2)[cc], Irreducible polynomials, Irreducible trinomials, Mersenne exponents, Mersenne numbers, Primitive polynomials, Primitive trinomials",

author = "Brent, {Richard P.} and Paul Zimmermann",

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doi = "10.1090/S0025-5718-08-02170-4",

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AU - Zimmermann, Paul

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AB - We exhibit ten new primitive trinomials over GF(2) of record degrees 24036 583, 25 964951, 30402 457, and 32 582 657. This completes the search for the currently known Mersenne prime exponents.

KW - GF(2)[cc]

KW - Irreducible polynomials

KW - Irreducible trinomials

KW - Mersenne exponents

KW - Mersenne numbers

KW - Primitive polynomials

KW - Primitive trinomials

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U2 - 10.1090/S0025-5718-08-02170-4

DO - 10.1090/S0025-5718-08-02170-4

M3 - Article

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VL - 78

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EP - 1199

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 266

ER -

Ten new primitive binary trinomials

Abstract

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