A213052 Increasing sequence of primes p such that all of 2,3,5,...,prime(n) are primitive roots mod p.

3, 5, 53, 173, 293, 2477, 9173, 22613, 27653, 61613, 74093, 92333, 170957, 360293, 679733, 847997, 2004917, 69009533, 76553573, 138473837, 237536213, 777133013, 883597853, 1728061733, 2050312613, 5534091197, 9447241877, 49107823133, 65315700413

Offset

1,1

Comments

a(32) > 10^12. - Dana Jacobsen, Jul 13 2018

Links

Dana Jacobsen, Table of n, a(n) for n = 1..31

Prog

(PARI)
N=10^10;
default(primelimit, N);
A=2;
{ forprime (p=3, N,
    q = 1;
    forprime (a=2, A,
        if ( znorder(Mod(a, p)) != p-1,  q=0; break() );
    );
    if ( q, A=nextprime(A+1); print1(p, ", ") );
); }
(Perl)
use Math::Prime::Util ":all";
my($N, $A, $p, $a, @P7) = (10**11, 2);
forprimes { $p=$_;
  if (   is_primitive_root(2, $p)
      && ($A < 3 || is_primitive_root(3, $p))
      && ($A < 5 || is_primitive_root(5, $p))
      && ($A < 7 || vecall { is_primitive_root($_, $p) } @P7)
    ) {
      print "$p\n";
      $A = next_prime($A);
      push @P7, $A if $A >= 7;
    }
} 3, $N;
# Dana Jacobsen, Jul 11 2018

Crossrefs

Sequence in context: A260226 A101149 A056260 * A355016 A260223 A260225

Adjacent sequences: A213049 A213050 A213051 * A213053 A213054 A213055

Keyword

nonn,hard

Author

Joerg Arndt, Jun 03 2012

Extensions

a(20)-a(27) from Joerg Arndt, Apr 10 2016

a(28)-a(29) from Dana Jacobsen, Jul 11 2018

Status

approved