It’s crazy to think that every single key pair already exists, but only minuscule fraction will ever be discovered.
Discussion
The wonders of combinatorics
I sometimes wonder if the government is running a massive project to search as many as they can. Not just to get bitcoin keys, but that would be a nice perk.
I mean they could try, it's not a very viable project though.
To put it in perspective, if every satoshi that could ever exist was in it's own address, there would only ever be 2.1^15 addresses. With 2^160 possible addresses, there's 7.9^28 times as many addresses as there are satoshis. Not too mention, even if it was feasible to do this, the amount of energy required would be astronomical and way out of the scope of human civilization as a whole let alone a rogue nation state.
The incentives are there so that if you have that much hash power, you'll just mine and benefit that way. Not try to steal others bitcoin.
And this is an extreme example because obviously single satoshis don't belong to their own address. I didn't look up how many addresses actually hold a balance. It's probably about 100 million or so.
Yeah, I was thinking more along the lines of it's still possible to get lucky. But you're right, it's a complete waste of energy.