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Abstract: this paper, we wanted a simple analytical condition, like that for quadratic polynomials, which would determine the number of roots a cubic polynomial f(x) has modulo q and, in particular, determine when f(x) is irreducible modulo q. Then we could search for irreducible cubics that produce numerous primes in much the same way that Lehmer, Shanks, Fung and Williams did for quadratics. Here, of course, we would apply Hardy and Littlewood's Conjecture H which is formulated in terms of the number... (Update)
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BibTeX entry: (Update)
@misc{ mott-primeproducing,
author = "Joe L. Mott and KERMIT ROSE",
title = "Prime-Producing Cubic Polynomials",
url = "citeseer.ist.psu.edu/403593.html" }
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