A059230 Primes p such that x^61 = 2 has no solution mod p.

367, 733, 977, 1709, 1831, 2441, 3539, 4027, 4271, 4637, 4759, 5003, 5857, 6101, 6833, 7321, 7687, 8053, 8297, 8419, 8663, 9029, 9151, 9883, 10859, 12323, 12689, 13177, 13421, 14153, 14519, 15373, 15739, 16349, 17203, 17569, 18301, 18911

Offset: 1

Author

Klaus Brockhaus, Jan 20 2001

Keywords

• nonn
• easy

Comments

Presumably this is also Primes congruent to 1 mod 61 (A212378). - N. J. A. Sloane, Jul 11 2008

Complement of A216884 relative to A000040. - Vincenzo Librandi, Sep 20 2012

Regarding the first comment, the smallest counterexample is the prime 34039: 34039 == 1 (mod 61), but 1155^61 == 2 (mod 34039), therefore this prime is not in the sequence. - Bruno Berselli, Sep 20 2012

Links

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

Crossrefs

Cf. A000040, A058853, A212378.

Programs

Magma

[p: p in PrimesUpTo(19000) | forall{x: x in ResidueClassRing(p) | x^61 ne 2} ]; // Vincenzo Librandi, Sep 20 2012

Mathematica

ok[p_]:= Reduce[Mod[x^61 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[5000]], ok] (* Vincenzo Librandi, Sep 20 2012 *)