A323577 Primes p such that 2 is a primitive root modulo p while 2048 is not.

67, 419, 661, 859, 947, 1123, 1277, 1453, 2069, 2267, 2333, 2531, 2707, 2861, 3037, 3323, 3499, 3851, 3917, 4093, 4357, 4621, 4973, 5171, 5501, 6029, 6469, 6491, 6733, 7019, 7283, 7349, 7459, 7547, 7789, 7877, 8053, 8669, 8867, 8933, 9901, 9923, 10099, 10253, 10891, 10979

Offset: 1

Author

Jianing Song, Aug 30 2019

Keywords

• nonn

Comments

Primes p such that 2 is a primitive root modulo p (i.e., p is in A001122) and that p == 1 (mod 11).

According to Artin's conjecture, the number of terms <= N is roughly ((10/109)*C)*PrimePi(N), where C is the Artin's constant = A005596, PrimePi = A000720. Compare: the number of terms of A001122 that are no greater than N is roughly C*PrimePi(N).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Artin's constant.
• Wikipedia, Artin's conjecture on primitive roots.

Crossrefs

Cf. A001122, A005596, A000720.

Primes p such that 2 is a primitive root modulo p and that p == 1 (mod q): A307627 (q=3), A307628 (q=5), A323576 (q=7), this sequence (q=11), A323590 (q=13).

Programs

PARI

forprime(p=3, 12000, if(znorder(Mod(2, p))==(p-1) && p%11==1, print1(p, ", ")))