Mining Bitcoin Wallet's Private Keys Instead of Blocks
To mine a block it is "enough" to guess the nonce that results in a hash compatible with the current difficulty level.

To guess a private key to a specific wallet you need on average 2^255 tries. Even the simple act of counting (not checking if that number is a key to some btc, just counting) from 0 to 2^255 with an ideal binary counter requires more energy than that provided by converting the whole mass of the Sun into energy.
Not impossibile, "just" infeasible 

Even if you are fine by guessing a private key to a random wallet out of a few million the amount of tries to do is not that much different in absolute terms and the reasoning still applies.

Google returns many funny trivia about how really immense is the keyspace, some with elaborate calculations too, such as that if we made a book with 255 keys per page containing all the possible keys that book would have 904625697166532776746648320380374280100293470930272690489102837043110636675 pages. (www.directory.io) 

Anyway, there is a project named "large bitcoin collider" that tries to guess private keys, obviously with "not much" success... (https://lbc.cryptoguru.org/about)