It seems intuitively clear that the twin prime constant $$ C_2 = \prod_{p > 2} \left(1-\frac{1}{(p-1)^2} \right) \approx 0.66016 $$ is irrational.
Can anyone please give a reference to a short proof of this (e.g. in an introductory number theory textbook)?
If this is in fact an open problem, could you please give a reference to some source explicitly stating so?