Can anyone come up with an interesting consequence of the Twin Prime Conjecture being true?

The twin prime problem is the tip of an iceberg. Settling it might help us decide whether, for all even $k$, there are infinitely many pairs of primes differing by $k$, even whether there are infinitely many pairs of consecutive primes differing by $k$, and that might shed light on the question of whether for every admissible $m$-tuple $(a_1,a_2,\dots,a_m)$ there are infinitely many $n$ such that all of the numbers $n+a_1,n+a_2,\dots,n+a_m$ are prime, and that might give us some insight into Schinzel's Hypothesis H (q.v.).

Don't know what application it will serve in the real world but long back out of curiosity, I wanted to find the asymptotic expansion of the $n$-th twin prime $q_n$ assuming the twin prime conjecture. I got something like

$$ q_n \sim \frac{n\log^2 n}{C}\bigg(1 + \frac{2\log\log n - 1}{\log n - 2}\bigg)^2 $$ where $C$ is twice the twin prime constant.