A377172 Primes p such that -3/2 is a primitive root modulo p.

17, 23, 37, 41, 43, 47, 67, 89, 109, 113, 137, 139, 157, 163, 167, 191, 229, 233, 239, 257, 263, 277, 283, 311, 349, 353, 359, 379, 383, 397, 421, 449, 479, 503, 521, 523, 541, 547, 569, 571, 593, 599, 613, 619, 641, 647, 661, 719, 733, 739, 743, 757, 761, 787, 809, 811, 839, 853, 857, 859, 863, 877, 887, 911, 929, 953, 977, 983

Offset: 1

Author

Jianing Song, Oct 18 2024

Keywords

• nonn
• easy

Comments

If p is a term in this sequence, then -3/2 is not a square modulo p (i.e., p is in A191059).

Conjecture: this sequence has relative density equal to Artin's constant (A005596) with respect to the set of primes.

Links

• Wikipedia, Artin's conjecture on primitive roots.
• Index entries for primes by primitive root

Crossrefs

Primes p such that +a/2 is a primitive root modulo p: A320384 (a=3), A377174 (a=5), A377176 (a=7), A377178 (a=9).

Primes p such that -a/2 is a primitive root modulo p: this sequence (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).

Cf. A191059, A005596.

Programs

PARI

forprime(p=5, 10^3, if(znorder(Mod(-3/2, p))==p-1, print1(p, ", ")));