Is this a known conjecture or theorem:
Among primes in the form $ax + b$ where $a, b$ are coprime (per Dirichlet's theorem on arithmetic progressions), $x$ is prime at least once.
Is this a known question? An answered question? Is it provable?
I'm specifically looking at this: $Px + 2$ where $P$ is prime. $P$ and $2$ are coprime, obviously. $Px + 2$ is prime infinitely often; $x$ has to be odd; does $x$ have to be prime at least once?