$p(n)/\log p(n)={}$prime

Question

A little item for anyone who wants to test their new exaflop machine. Given some $\operatorname{prime}(n)/\log\operatorname{prime}(n)={}$as near as possible to a prime $q,$ for both log base $10$ and base $e,$ what is $\operatorname{prime}(n)$? Near as possible means the minimum difference from either above or below $q;$ thus $126.9999$ or $127.00001$ would be considered to be very close to prime $127.$