How often is $\lfloor e^{\frac{P}{\log(P)}} \rfloor\in\Bbb P?$

Question

I am trying to find more solutions for $P\in \Bbb P.$ So far I've found one solution, namely, $P=2 \implies 17.$

$\lfloor e^{\frac{P}{\log(P)}} \rfloor\in\Bbb P$

Are there any other solutions? I would expect there to be more than one solution.

Answer 1

there is also a solution for $p=2539$, that gives the $141$-digit prime number

$45254910559759849762222771225911176650840872909151339307437267111370555371623\\3918994350899471803697431194890625981348468878260730825307902129$