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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 (list; graph; refs; listen; history; text; internal format)
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.
J. Alexander. Irreducibility criteria for polynomials with non-negative integer coefficients. Master's Thesis, University of South Carolina. 1987. Cited in Dunn 2014.
Charles R Greathouse IV, Table of n, a(n) for n = 3..20
J. Brillhart, M. Filaseta, and A. Odlyzko, On an irreducibility theorem of A. Cohn, Canad. J. Math. 33 (1981), pp. 1055-1059.
Michael Filaseta, Irreducibility criteria for polynomials with nonnegative coefficients, Canad. J. Math. 40 (1988), pp. 339-351.
Michael Filaseta and Samuel Gross, 49598666989151226098104244512918, J. Number Theory 137 (2014), pp. 16-49.
Sequence in context: A232381 A109183 A284872 * A251518 A031793 A234765

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Last modified December 4 16:44 EST 2023. Contains 367563 sequences. (Running on oeis4.)