On the least prime primitive root modulo a prime

Paszkiewicz, A.; Schinzel, A.

doi:10.1090/S0025-5718-02-01370-4

On the least prime primitive root modulo a prime
HTML articles powered by AMS MathViewer

by A. Paszkiewicz and A. Schinzel;

Math. Comp. 71 (2002), 1307-1321

DOI: https://doi.org/10.1090/S0025-5718-02-01370-4

Published electronically: January 17, 2002

PDF | Request permission

Abstract:

We derive a conditional formula for the natural density $E(q)$ of prime numbers $p$ having its least prime primitive root equal to $q$, and compare theoretical results with the numerical evidence.

References

C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
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
Leonardo Cangelmi and Francesco Pappalardi, On the $r$-rank Artin conjecture. II, J. Number Theory 75 (1999), no. 1, 120–132. MR 1677559, DOI 10.1006/jnth.1998.2319
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
Władysław Narkiewicz, Elementary and analytic theory of algebraic numbers, 2nd ed., Springer-Verlag, Berlin; PWN—Polish Scientific Publishers, Warsaw, 1990. MR 1055830
Francesco Pappalardi, On minimal sets of generators for primitive roots, Canad. Math. Bull. 38 (1995), no. 4, 465–468. MR 1360597, DOI 10.4153/CMB-1995-068-4
Francesco Pappalardi, On the $r$-rank Artin conjecture, Math. Comp. 66 (1997), no. 218, 853–868. MR 1377664, DOI 10.1090/S0025-5718-97-00805-3
John W. Wrench Jr., Evaluation of Artin’s constant and the twin-prime constant, Math. Comp. 15 (1961), 396–398. MR 124305, DOI 10.1090/S0025-5718-1961-0124305-0