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Numerical calculation of the density of prime numbers with a given least primitive root

Authors: A. Paszkiewicz and A. Schinzel
Journal: Math. Comp. 71 (2002), 1781-1797
MSC (2000): Primary 11Y16; Secondary 11A07, 11M26
Published electronically: November 28, 2001
MathSciNet review: 1933055
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Abstract: In this paper the densities $D(i)$ of prime numbers $p$ having the least primitive root $g(p)=i$, where $i$ is equal to one of the initial positive integers less than 32, have been numerically calculated. The computations were carried out under the assumption of the Generalised Riemann Hypothesis. The results of these computations were compared with the results of numerical frequency estimations.

References [Enhancements On Off] (What's this?)

  • 1. E. Bach, Comments on search procedures for primitive roots, Math. Comp. 66 (1997), 1719-1727. MR 98a:11187
  • 2. R. N. Buttsworth, A general theory of inclusion-exclusion with application to the least primitive root problem, and other density question, Ph.D. Thesis, University of Queensland, Queensland, 1983.
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Additional Information

A. Paszkiewicz
Affiliation: Warsaw University of Technology, Institute of Telecommunications, Division of Telecommunications Fundamental, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland

A. Schinzel
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warsaw, Poland

Keywords: Prime, generators, primitive roots, extended Riemann hypothesis
Received by editor(s): November 29, 1999
Received by editor(s) in revised form: December 26, 2000
Published electronically: November 28, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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