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On Euler polynomials and Rabinowitsch polynomials. (English) Zbl 1272.11107

The author extends results of this reviewer on prime-producing quadratic polynomials. Specifically, the notion of prime production length introduced by this reviewer in [Am. Math. Mon. 104, No. 6, 529–544 (1997; Zbl 0886.11053)], is used to obtain exact such lengths for certain discriminants, especially those of narrow Richaud-Degert type, namely of the form \(r^2+1\) and \(r^2+4\). The bounds on prime-production length which the author improves are those given in this reviewer’s work [“The Rabinowitsch-Mollin-Williams theorem revisited”, Int. J. Math. Math. Sci. 2009, Article ID 819068, 14 p. (2009; Zbl 1290.11151)]. At the end of the paper, the author leaves a conjecture on the primality of integers \(n\equiv 3\pmod 4\) related to the factors of \(y^2-y+(n+1)/4\) all being quadratic residues modulo \(n\), seemingly a tractable open question.

MSC:

11N32 Primes represented by polynomials; other multiplicative structures of polynomial values
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