Is there any non-identity monotonically increasing one-one univariate function that takes prime number as input and generates prime number as output ?
The asymptotic complexity to calculate output must me $O(1)$ (assume exponentiation is $O(1)$ operaton).
Output prime must be greater than input prime for all input primes.
$f(n)$ $=$ $\lfloor$$A^{3^n}$$\rfloor$, where A is OEIS A051021 (~1.3).
https://en.wikipedia.org/wiki/Mills'_constant
https://oeis.org/A051021
(Though, it sounds like you're using this for a practical application, and I'm pretty sure this isn't practical.)