A040984 Primes p such that x^23 = 2 has no solution mod p.

47, 139, 277, 461, 599, 691, 829, 967, 1013, 1151, 1289, 1381, 1427, 1657, 1933, 1979, 2347, 2393, 2531, 3037, 3083, 3221, 3313, 3359, 3727, 3911, 4003, 4049, 4463, 4831, 4877, 4969, 5107, 5521, 5659, 5843, 5981, 6073, 6211, 6257, 6763, 6947, 7039, 7177

Offset: 1

Author

Klaus Brockhaus, Jan 20 2001

Keywords

• nonn
• easy

Comments

Contribution from Charles R Greathouse IV, Sep 12 2012: (Start)

Complement of A049555 relative to A000040.

Terms of A212374 which are not in this sequence: 5153, 18539, 20747, 49681, 51199, 51797, 55201, 70381, .... (End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A049555.

Cf. A212374.

Programs

Magma

[p: p in PrimesUpTo(8000) | forall{x: x in ResidueClassRing(p) | x^23 ne 2}]; // Vincenzo Librandi, Aug 21 2012

Mathematica

Select[Prime[Range[PrimePi[7200]]], ! MemberQ[PowerMod[Range[#], 23, #], Mod[2, #]] &] (* T. D. Noe, Sep 13 2012 *)
 ok[p_]:=Reduce[Mod[x^23 - 2, p]==0, x, Integers]==False; Select[Prime[Range[25000]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

PARI

select(n->!ispower(Mod(2,n),23),primes(1000)) \\ Charles R Greathouse IV, Sep 12 2012