As the title asks, is it possible to guess a privkey/generate an existing wallet's privkey? I'm quite interested about how mining for a bitcoin address works. Is it kind of the same thing as mining a block, guessing combinations of numbers and letters (the privkey) to unlock the code (wallet address), or is it some other kind of algorithm?

I've used vanity miner before, and I've tried guessing an existing address, but according do vanitygen, it takes more than a billion years on average to solve. Assuming I was lucky enough to mine the exact same address, could I get the privkey?