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

%I #8 Oct 23 2024 20:27:00

%S 11,17,23,47,59,73,101,103,109,113,137,139,149,167,179,211,223,229,

%T 233,257,263,269,313,337,349,353,367,379,383,389,419,421,433,461,487,

%U 499,503,509,593,607,617,647,659,661,673,727,743,811,821,823,829,857,859,863,887,941,953,967,971,977,983

%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 A038880).

%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) 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), this sequence (a=5), A377176 (a=7), A377178 (a=9).

%Y Primes p such that -a/2 is a primitive root modulo p: A377172 (a=3), A377175 (a=5), A377177 (a=7), A377179 (a=9).

%Y Cf. A038880, A005596.

%K nonn,easy

%O 1,1

%A _Jianing Song_, Oct 18 2024