

A253280


Greatest k such that a polynomial f(x) with integer coefficients between 0 and k is irreducible if f(n) is prime.


2



3795, 8925840, 56446139763, 568059199631352, 4114789794835622912, 75005556404194608192050, 1744054672674891153663590400, 49598666989151226098104244512918, 1754638089240473418053140582402752512
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OFFSET

3,1


COMMENTS

This is an extension of Cohn's irreducibility theorem, which is a(10) >= 9.
Brillhart, Filaseta, & Odlyzko show that a(n) >= n1; 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.


REFERENCES

J. Alexander. Irreducibility criteria for polynomials with nonnegative integer coefficients. Master's Thesis, University of South Carolina. 1987. Cited in Dunn 2014.


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CROSSREFS



KEYWORD

nonn,nice


AUTHOR



STATUS

approved



