So a couple of days ago the $17$ million digit number $2^{57885161}-1$ was beaten by the $22$ million digit number $2^{74207281}-1$ at being the largest known prime number.
Are there any specific (purely mathematical) implications of the fact that this particular number is prime? In particular, does this resolve something other than the question if $2^{74207281}-1$ is prime, in the style of some newly discovered theorem resolving previous conjectures? Is it perhaps a counterexample to something so far believed to be true?
Edit: I'm aware of the many non-(strictly mathematical) practical implications and reasons to continue the search for large primes (cryptography etc), but I'm not aware of any strictly mathematical uses of particular numbers being prime, which is why (and what) I'm asking.