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%I #24 Sep 08 2022 08:45:02
%S 709,827,1063,1181,1889,2243,2833,3187,3541,3659,4013,4603,4721,4957,
%T 5783,6373,6491,7789,7907,8969,9323,9677,10267,10739,11093,11329,
%U 11801,12037,12391,13099,13217,13807,14633,14869,16993,19471,20297,20533
%N Primes p such that x^59 = 2 has no solution mod p.
%C 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
%C Complement of A216886 relative to A000040. - _Vincenzo Librandi_, Sep 20 2012
%H Zak Seidov, <a href="/A059312/b059312.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Prime[Range[PrimePi[21000]]], ! MemberQ[PowerMod[Range[#], 59, #], Mod[2, #]] &] (* _Bruno Berselli_, Sep 20 2012 *)
%t ok[p_] := Reduce[Mod[x^59 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)
%o (Magma) [p: p in PrimesUpTo(21000) | forall{x: x in ResidueClassRing(p) | x^59 ne 2}]; // _Bruno Berselli_, Sep 20 2012
%Y Cf. A000040, A058853, A216315, A216886.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 25 2001