A001124 Primes with 5 as smallest primitive root.

23, 47, 73, 97, 103, 157, 167, 193, 263, 277, 307, 383, 397, 433, 503, 577, 647, 673, 683, 727, 743, 863, 887, 937, 967, 983, 1033, 1093, 1103, 1153, 1163, 1223, 1367, 1487, 1543, 1583, 1607, 1777, 1823, 1847, 1933, 1993, 2003, 2017, 2063, 2087, 2113, 2203, 2207

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.
• M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 57.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for primes by primitive root

Crossrefs

Cf. A001122, A001123, A001125, etc.

Programs

Mathematica

<< NumberTheory`NumberTheoryFunctions`; Prime[ Select[ Range[200], PrimitiveRoot[ Prime[ # ] ] == 5 & ] ]
(* first load *) << NumberTheory`NumberTheoryFunctions` (* then *) Select[ Prime@Range@300, PrimitiveRoot@# == 5 &] (* Robert G. Wilson v, May 11 2001 *)
Select[Prime[Range[350]],PrimitiveRoot[#]==5&] (* The PrimitiveRoot function is now part of Mathematica's core, so no add-in needs to be loaded before calling it *) (* Harvey P. Dale, Dec 06 2014 *)

Python

from itertools import islice
from sympy import nextprime, primitive_root
def A001124_gen(): # generator of terms
    p = 5
    while (p:=nextprime(p)):
        if primitive_root(p)==5:
            yield p
A001124_list = list(islice(A001124_gen(),30)) # Chai Wah Wu, Feb 13 2023

Extensions

More terms from Robert G. Wilson v, May 10 2001