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

Author(s): A. Paszkiewicz; A. Schinzel.
Journal: Math. Comp. 71 (2002), 1781-1797.
MSC (2000): Primary 11Y16; Secondary 11A07, 11M26
Posted: November 28, 2001
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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:

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.
3.
P.D.T.A. Elliott, L. Murata, On the average of the least primitive root modulo $p$, J. London Math. Soc. (2) 56 (1997), 435-454. MR 98m:11094
4.
K. R. Matthews, A generalisation of Artin's conjecture for primitive roots, Acta Arith. 29 (1976), 113-146. MR 53:313

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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
Email: anpa@tele.pw.edu.pl

A. Schinzel
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-950 Warsaw, Poland
Email: schinzel@impan.gov.pl

DOI: 10.1090/S0025-5718-01-01382-5
PII: S 0025-5718(01)01382-5
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
Posted: November 28, 2001
Copyright of article: Copyright 2001, American Mathematical Society

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