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A213052 Increasing sequence of primes p such that all of 2,3,5,...,prime(n) are primitive roots mod p. 7
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 (list; graph; refs; listen; history; text; internal format)
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 * A260223 A260225 A020462

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

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Last modified February 28 03:40 EST 2020. Contains 332321 sequences. (Running on oeis4.)