Does the Riemann-Hypothesis imply the Twin-Prime-Conjecture?

I'd say no. Many authors state that RH would tell us nothing more (about prime gaps) than $p_{n+1}-p_n \in \text{O}(\sqrt{p_n}\log p_n)$, which obviously doesn't imply TPC, and so it should not be unsafe to say RH doesn't imply TPC.