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Primes p such that -5/2 is a primitive root modulo p.
6

%I #8 Oct 23 2024 20:26:57

%S 3,17,31,43,67,71,73,79,83,101,107,109,113,137,149,163,191,199,227,

%T 229,233,239,257,269,271,283,307,311,313,337,347,349,353,359,389,421,

%U 431,433,439,443,461,467,479,509,547,563,587,593,599,617,631,661,673,683,719,821,827,829,839,857,907,911,919,941,947,953,977

%N Primes p such that -5/2 is a primitive root modulo p.

%C If p is a term in this sequence, then -5/2 is not a square modulo p (i.e., p is in A296925).

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots">Artin's conjecture on primitive roots</a>.

%H <a href="/index/Pri#primes_root">Index entries for primes by primitive root</a>

%o (PARI) print1(3, ", "); forprime(p=7, 10^3, if(znorder(Mod(-5/2, p))==p-1, print1(p, ", ")));

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

%Y Primes p such that -a/2 is a primitive root modulo p: A377172 (a=3), this sequence (a=5), A377177 (a=7), A377179 (a=9).

%Y Cf. A296925, A005596.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Oct 18 2024