W.S. Brown, Reducibility properties of polynomials over the rationals, Amer. Math. Monthly 70 (1963), 965-969.  Home/Search   Document Not in Database   Summary   Related Articles

....that f(x) will produce any primes at all, much less, an initial string of prime values. For example, the irreducible polynomial f(x) x 2 x 4 is such that its values are even for every integral x and never equals 2. Indeed, since the average polynomial of degree d is irreducible [Bro], there must be other properties that contribute to the ability to produce primes. Thus, we pose the question in reverse: If f(x) is irreducible, what additional properties must f(x) satisfy in order to produce a high density of primes in an interval and, in particular, what properties will insure ....

W.S. Brown, Reducibility properties of polynomials over the rationals, Amer. Math. Monthly 70 (1963), 965-969.

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