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> Let $p$ be a prime number. Is there a prime number $q$ such that $p$ is a primitive root of $q$?
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on prime numbers which are primitive roots of a prime
Gupta and R. Murta showed that there were infinitely many primes $p$ for which there are infinitely many $q$. Heath-Brown generalized this to show that there are at most two prime numbers $p$ for which there are not infinitely many $q$ that they are primitive roots modulo $q$.


Heath-Brown, D. R.(4-OXM)
Artin's conjecture for primitive roots. 
Quart. J. Math. Oxford Ser. (2) 37 (1986), no. 145, 27–38. 
11A07 (11N13 11N35) 


Gupta, Rajiv(1-IASP); Murty, M. Ram(3-MGL)
A remark on Artin's conjecture. 
Invent. Math. 78 (1984), no. 1, 127–130. 
11A07 


