2021
DOI: 10.48550/arxiv.2105.03915
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Block designs and prime values of polynomials

Gareth A. Jones,
Alexander K. Zvonkin

Abstract: A recent construction by Amarra, Devillers and Praeger of block designs with specific parameters depends on certain quadratic polynomials, with integer coefficients, taking prime power values. The Bunyakovsky Conjecture, if true, would imply that each of them takes infinitely many prime values, giving an infinite family of block designs with the required parameters. We have found large numbers of prime values of these polynomials, and the numbers found agree very closely with the estimates for them provided by… Show more

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