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A059644 Primes p such that x^58 = 2 has no solution mod p. 2
3, 5, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 233, 251, 269, 277, 283, 293, 307, 317, 331, 347, 349, 373, 379, 389, 397, 419, 421, 443, 461, 467, 491, 499, 509, 523, 541, 547, 557 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Complement of A049590 relative to A000040.

LINKS

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

MATHEMATICA

ok[p_] := Reduce[Mod[x^58 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[120]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

PROG

(MAGMA) [p: p in PrimesUpTo(600) | not exists{x: x in ResidueClassRing(p) | x^58 eq 2}]; // 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, 58), print1(p, ", ")));

/* Joerg Arndt, Sep 21 2012 */

CROSSREFS

Cf. A000040, A049590.

Sequence in context: A059314 A059336 A059350 * A059646 A319041 A003629

Adjacent sequences:  A059641 A059642 A059643 * A059645 A059646 A059647

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Feb 02 2001

STATUS

approved

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Last modified June 15 02:56 EDT 2021. Contains 345042 sequences. (Running on oeis4.)