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Artin prime producing quadratics

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Abstract

Fix an integerg. The primesp such thatg is a primitive root forp are calledArtin primes. Using a mixture of heuristics, well-known conjectures and rigorous arguments an algorithm is given to find quadratics that produce many Artin primes. Using this algorithmY. Gallot has found ag and a quadraticf such that the first 31082 primes produced byf haveg as a primitive root. There is a connection with finding integersd such thatL(2, (d/·)) is small.

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Deutschland

    P. Moree

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  1. P. Moree
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Correspondence to P. Moree.

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Communicated by: B. Richter

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Moree, P. Artin prime producing quadratics. Abh. Math. Sem. Univ. Hamburg 77, 109–127 (2007). https://doi.org/10.1007/BF03173492

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  • DOI: https://doi.org/10.1007/BF03173492

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