I am interested in the following question:

Is it known that $2$ is a primitive root modulo $p$ for infinitely many primes $p$?

There is some information about Artin's conjecture in [Wikipedia][1].
I need to know if it is up-to-date and if one can say something about the case $n=2$.

  [1]: https://en.wikipedia.org/w/index.php?title=Artin%27s_conjecture_on_primitive_roots&oldid=374854868