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Search: id:A001153
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| A001153 |
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Degrees of primitive irreducible trinomials: n such that 2^n - 1 is a Mersenne prime and x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some k with 0 < k < n.
(Formerly M0678 N0250)
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+0
6
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| 2, 3, 5, 7, 17, 31, 89, 127, 521, 607, 1279, 2281, 3217, 4423, 9689, 19937, 23209, 44497, 110503, 132049, 756839, 859433, 3021377, 6972593
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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None exist for the latest Mersenne prime, 13466917, so until a new Mersenne prime is discovered, this sequence is complete. - Paul Zimmermann, Sep 05 2002.
Also the list of "irreducible Mersenne trinomials" since here irreducible implies primitive.
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REFERENCES
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Kurita, Yoshiharu and Matsumoto, Makoto; Primitive t-nomials (t=3,5) over GF(2) whose degree is a Mersenne exponent <= 44497. Math. Comp. 56 (1991), no. 194, 817-821.
N. Zierler, On x^n+x+1 over GF(2). Information and Control 16 1970 502-505.
N. Zierler, Primitive trinomials whose degree is a Mersenne exponent. Information and Control 15 1969 67-69.
N. Zierler and J. Brillhart, On primitive trinomials (mod 2). Information and Control 13 1968 541-554.
N. Zierler and J. Brillhart, On primitive trinomials (mod 2), II. Information and Control 14 1969 566-569.
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LINKS
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R. P. Brent, Searching for primitive trinomials (mod 2)
R. P. Brent, Tables of trinomials
R. P. Brent, S. Larvala and P. Zimmermann, A fast algorithm for testing reducibility of trinomials ..., Math. Comp. 72 (2003), 1443-1452.
A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996; see p. 162.
Index entries for sequences related to trinomials over GF(2)
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CROSSREFS
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Cf. A002475, A000043, A073571, A073639, A057486, A073726.
For values of k see A074743.
Adjacent sequences: A001150 A001151 A001152 this_sequence A001154 A001155 A001156
Sequence in context: A103384 A103383 A103382 this_sequence A100532 A040149 A034970
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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Corrected and extended by Paul Zimmermann, Sep 05, 2002.
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