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

Paszkiewicz, A.; Schinzel, A.

doi:10.1090/S0025-5718-01-01382-5

Numerical calculation of the density of prime numbers with a given least primitive root
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by A. Paszkiewicz and A. Schinzel PDF

Math. Comp. 71 (2002), 1781-1797 Request permission

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

Eric Bach, Comments on search procedures for primitive roots, Math. Comp. 66 (1997), no. 220, 1719–1727. MR 1433261, DOI 10.1090/S0025-5718-97-00890-9
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.
P. D. T. A. Elliott and Leo Murata, On the average of the least primitive root modulo $p$, J. London Math. Soc. (2) 56 (1997), no. 3, 435–454. MR 1610435, DOI 10.1112/S0024610797005310
K. R. Matthews, A generalisation of Artin’s conjecture for primitive roots, Acta Arith. 29 (1976), no. 2, 113–146. MR 396448, DOI 10.4064/aa-29-2-113-146