TITLE: Does the Riemann-Hypothesis imply the Twin-Prime-Conjecture?
QUESTION [11 upvotes]: The Riemann hypothesis (https://en.wikipedia.org/wiki/Riemann_hypothesis)
is one of the most important conjectures in number theory. I read that the
Riemann hypothesis implies the Goldbach Conjecture and would allow much
better estimates for the prime-counting function.
What about the Twin-Prime-Conjecture ?
Would it follow from the Riemann-hypothesis ?

REPLY [2 votes]: Interestingly, as I recently learned from a popular Mathoverflow question, if the RH GRH is false in a specific way (it has Siegel zeros), that would imply the Twin Prime conjecture is true (!!)