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Instead of mining Bitcoins directly, couldn't one of these huge processing farms dedicate their processing power to instead discovering the private keys of the largest wallets on the ledger?

I realize randomly guessing private keys is unlikely. However unlikely though, it would seem you'd increase your likelihood for each additional guess and a mining farm could do a lot of guessing with 24 hours a day 365 days a year. And, any particular guess could be the lucky one that cracks the wallet.

I'm asking this question not because I want to do this. I'm asking it because "if I can think of it" someone else is probably already trying it.

Each day, this farm could query the top 10 wallets in the ledger and just do random private key guesses all day long. If these big accounts switched wallets each day, it wouldn't matter, a farm would be guessing on those new wallets constantly (what ever is top 10, at any given time, could be constantly randomly guessed at).

What prevents this?

Lonnie Best
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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)

Caterpillaraoz
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    Related on Crypto.SE: https://crypto.stackexchange.com/a/1160 – Caterpillaraoz Dec 16 '17 at 00:29
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    Despite all this, the very first random guess could be the lucky one. Bitcoin better hope that all psychics are fake too, else they'll start cracking wallets like walnuts! – Lonnie Best Jan 15 '22 at 09:30