A029932 Primes with record values of the least positive prime primitive root.

3, 7, 23, 41, 109, 191, 271, 2791, 11971, 31771, 190321, 2080597, 3545281, 4022911, 73189117, 137568061, 443571241, 565822531, 1160260711, 1622723341, 31552100581, 81651092041, 96736641541, 1867622877121, 5000346134911

Offset: 1

Author

Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

Keywords

• nonn
• nice

Comments

Other terms in the sequence: 39227234631271, 66597722601061 and 84054326426071 -Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 19 2008

Subsequence of A002230, considering only prime primitive roots. - M. F. Hasler, Jun 01 2018

References

• R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.
• A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XLV.

Links

• Tomás Oliveira e Silva, Counts of least primitive roots of prime numbers (Artin's conjecture)
• Tomás Oliveira e Silva, Least prime primitive roots
• A. Paszkiewicz and A. Schinzel, On the least prime primitive root modulo a prime, Math. Comp. 71 (2002), no. 239, 1307-1321.
• A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages]
• Index entries for primes by primitive root

Crossrefs

Cf. A060749, A002230, A084735.

Programs

Mathematica

(* This program is not suitable for computing more than a dozen terms. *) max = 10^8; pprQ[r_, p_] := Union[Table[PowerMod[r, i, p], {i, 1, p+1}]] == coprimes; ppr[p_] := With[{spr = PrimitiveRoot[p]}, If[PrimeQ[spr], spr, coprimes = Select[Range[p-1], CoprimeQ[#, p]&]; For[r = NextPrime[ spr], True, r = NextPrime[r], If[pprQ[r, p], Return[r]]]]]; Reap[ For[ record=1; p=3, p record, record = ppr1; Print["p = ", p, " ppr = ", record]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Feb 25 2016 *)

Extensions

Corrected by Jud McCranie, Jan 04 2001

2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 19 2008