A059312 Primes p such that x^59 = 2 has no solution mod p.

709, 827, 1063, 1181, 1889, 2243, 2833, 3187, 3541, 3659, 4013, 4603, 4721, 4957, 5783, 6373, 6491, 7789, 7907, 8969, 9323, 9677, 10267, 10739, 11093, 11329, 11801, 12037, 12391, 13099, 13217, 13807, 14633, 14869, 16993, 19471, 20297, 20533

Offset

1,1

Comments

This is not the same as "Primes congruent to 1 mod 59", A216315. The first missing number is A216315(27) = 11447. - Zak Seidov, Sep 03 2012

Complement of A216886 relative to A000040. - Vincenzo Librandi, Sep 20 2012

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Mathematica

Select[Prime[Range[PrimePi[21000]]], ! MemberQ[PowerMod[Range[#], 59, #], Mod[2, #]] &] (* Bruno Berselli, Sep 20 2012 *)
ok[p_] := Reduce[Mod[x^59 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok]  (* Vincenzo Librandi, Sep 20 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(21000) | forall{x: x in ResidueClassRing(p) | x^59 ne 2}]; // Bruno Berselli, Sep 20 2012

Crossrefs

Cf. A000040, A058853, A216315, A216886.

Sequence in context: A279747 A216402 A216315 * A114923 A057849 A199091

Adjacent sequences: A059309 A059310 A059311 * A059313 A059314 A059315

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 25 2001

Status

approved