A213050 Primes of the form 4*k+1 with primitive root +2.

5, 13, 29, 37, 53, 61, 101, 149, 173, 181, 197, 269, 293, 317, 349, 373, 389, 421, 461, 509, 541, 557, 613, 653, 661, 677, 701, 709, 757, 773, 797, 821, 829, 853, 877, 941, 1061, 1109, 1117, 1213, 1229, 1237, 1277, 1301, 1373, 1381, 1453, 1493, 1549, 1621

Offset: 1

Author

Joerg Arndt, Jun 03 2012

Keywords

• nonn

Comments

Primes p such that both +2 and -2 are primitive roots mod p.

A001122 is the union of A213050 and A213051.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A213051 (primes 4*k+3 with primitive root +2).

Cf. A001122 (primitive root +2), A007885 (primitive root +2 or -2).

Programs

Mathematica

Select[Prime[Range[300]], Mod[#, 4] == 1 && PrimitiveRoot[#, 2] == 2&] (* Jean-François Alcover, Jul 22 2018 *)

PARI

{ forprime (p=3, 10^4,
    rp = znorder(Mod(+2,p));
    rm = znorder(Mod(-2,p));
    if ( (rp==p-1) && (rm==p-1), print1(p,", ") );
);}