A059665 Primes p such that x^54 = 2 has no solution mod p, but x^6 = 2 has a solution mod p.

433, 919, 1423, 1999, 2017, 2143, 2287, 2791, 2953, 3457, 3889, 3943, 4177, 4519, 4663, 5113, 5167, 6679, 6967, 8713, 9631, 9649, 9721, 10009, 11287, 11863, 12241, 12583, 12799, 13177, 13591, 15913, 16057, 16111, 16561, 16921, 17551, 18127

Offset: 1

Author

Klaus Brockhaus, Feb 04 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..389

Crossrefs

A000040, A040992, A040993, A049550, A059666, A059664.

Programs

Magma

[p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^54 eq 2} and exists{x: x in ResidueClassRing(p) | x^6 eq 2}]; // Vincenzo Librandi, Sep 21 2012

Mathematica

Select[Prime[Range[PrimePi[20000]]], !MemberQ[PowerMod[Range[#], 54, #], Mod[2, #]] && MemberQ[PowerMod[Range[#], 6, #], Mod[2, #]] &] (* Vincenzo Librandi, Sep 21 2013 *)