Artin's Conjecture: There are infinitely many primes $p$ for which 2 is a primitive root, i.e., 2 generates the multiplicative group of ${\mathbb Z}/p{\mathbb Z}$.

The conjecture is actually a bit more general, but we should at least be able to say what happens with 2!

Artin's Conjecture: There are infinitely many primes $p$ for which 2 is a primitive root, i.e., 2 generates the multiplicative group of ${\mathbb Z}/p{\mathbb Z}$.

The conjecture is actually a bit more general, but we should at least be able to say what happens with 2! The OEIS lists the first several such primes.