A172058 Prime numbers p such that every prime divisor of p-1 is a primitive root modulo p.

3, 5, 19, 163, 379, 419, 827, 907, 1427, 1787, 1979, 1987, 2083, 2243, 2339, 2539, 2659, 2699, 3083, 3643, 3659, 4723, 5147, 5443, 5563, 5779, 6203, 6299, 6547, 6619, 6803, 6947, 7043, 7283, 7499, 7547, 7883, 7907, 8219, 8387, 8539, 8563, 8627, 8923

Offset

1,1

Comments

The sequence is probably infinite. If so, then there are infinitely many primes for which 2 is a primitive root (A001122).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

m = 1; s = {}; While[Prime[m] < 10000, m = m + 1; p = Prime[m]; pf = FactorInteger[p - 1]; L = Length[pf]; j = 0; While[j < L, j = j + 1; q = First[pf[[j]]]; If[MultiplicativeOrder[q, p] == p - 1, , j = L + 1]; If[j == L, s = {s, p}, ] ] ]; s = Flatten[s]

Crossrefs

Cf. A001122.

Sequence in context: A294382 A201108 A291920 * A303937 A062577 A144743

Adjacent sequences: A172055 A172056 A172057 * A172059 A172060 A172061

Keyword

nonn

Author

Emmanuel Vantieghem, Jan 24 2010

Status

approved