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A253280
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Greatest k such that a polynomial f(x) with integer coefficients between 0 and k is irreducible if f(n) is prime.
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2
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3795, 8925840, 56446139763, 568059199631352, 4114789794835622912, 75005556404194608192050, 1744054672674891153663590400, 49598666989151226098104244512918, 1754638089240473418053140582402752512
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OFFSET
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3,1
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COMMENTS
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This is an extension of Cohn's irreducibility theorem, which is a(10) >= 9.
Brillhart, Filaseta, & Odlyzko show that a(n) >= n-1; Filaseta shows that 10^30 < a(10) < 62 * 10^30.
a(10) is due to Filaseta & Gross, a(8)-a(9) and a(11)-a(20) to Cole, and a(3)-a(7) to Dunn. Dunn proves that 7 <= a(2) <= 9, but its value is not known at present.
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REFERENCES
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J. Alexander. Irreducibility criteria for polynomials with non-negative integer coefficients. Master's Thesis, University of South Carolina. 1987. Cited in Dunn 2014.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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