A059647 Primes p such that x^63 = 2 has no solution mod p.

7, 13, 19, 29, 37, 43, 61, 67, 71, 73, 79, 97, 103, 109, 113, 127, 139, 151, 163, 181, 193, 197, 199, 211, 239, 241, 271, 281, 307, 313, 331, 337, 349, 367, 373, 379, 409, 421, 433, 449, 463, 487, 491, 523, 541, 547, 571, 577, 607, 613, 617, 619, 631, 659

Offset: 1

Author

Klaus Brockhaus, Feb 02 2001

Keywords

• nonn
• easy

Comments

Complement of A049595 relative to A000040.

Links

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

Crossrefs

Cf. A000040, A049595.

Programs

Magma

[p: p in PrimesUpTo(700) | not exists{ x : x in ResidueClassRing(p) | x^63 eq 2}]; // Vincenzo Librandi, Sep 21 2012

Mathematica

ok[p_] := Reduce[Mod[x^63 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2150]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

PARI

N=10^4;  default(primelimit,N);
ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
forprime(p=2,N, if (! ok(p,2,63),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */