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A059312
Primes p such that x^59 = 2 has no solution mod p.
7
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
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
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jan 25 2001
STATUS
approved