A213051 Primes of the form 4*k+3 with primitive root +2.

3, 11, 19, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 347, 379, 419, 443, 467, 491, 523, 547, 563, 587, 619, 659, 787, 827, 859, 883, 907, 947, 1019, 1091, 1123, 1171, 1187, 1259, 1283, 1291, 1307, 1427, 1451, 1483, 1499, 1523, 1531, 1571, 1619, 1667, 1747

Offset: 1

Author

Joerg Arndt, Jun 03 2012

Keywords

• nonn

Comments

Primes with primitive root +2 where -2 is not a primitive root.

A001122 is the union of A213050 and A213051.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Christian Elsholtz, Almost all primes have a multiple of small Hamming weight, arXiv:1602.05974 [math.NT], 2016. See p. 6.

Crossrefs

Cf. A213050 (primes 4*k+1 with primitive root +2), A001122 (primitive root +2).

Programs

Mathematica

Select[Prime[Range[300]], Mod[#, 4] == 3 && 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,", ") );
);}