Finding the smallest prime that is larger than $10^{100}$ or $10^{10^{10}}$ Is there a known tractable way to find the smallest prime number that is larger than $10^{100}$? I'm asking because I want to use this as an example for a task that requires an incredible amount of computation power, and I don't want to embarrass myself :)

Here's an easy fix to the OP's problem: instead of $10^{100}$, use $10^{10^{10}}$. It's only slightly longer to write, but much, much larger as a number (and the prime question extremely hard to answer).