Let $q$ be a prime number, and let $k={\rm ord}_q\ 2$, the multiplicative order of 2 modulo $q$. Is there a known upper bound (a function depending on $p$, maybe) to the number of primes $p$ such that $k={\rm ord}_p\ 2$?

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Let $q$ be a prime number, and let $k={\rm ord}_q\ 2$, the multiplicative order of 2 modulo $q$. Is there a known upper bound (a function depending on $p$, maybe) to the number of primes $p$ such that $k={\rm ord}_p\ 2$?

On the order of finitely generated subgroups$\ldots$, and I'd be happy to say more if you're fine with assuming GRH.) $\endgroup$ – Vesselin Dimitrov Nov 25 '18 at 14:34