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I understand how difficult it would be to brute force a specific bitcoin address' private key.

I'm wondering out of curiosity though, with bitcoin being adopted so rapidly, will there ever be computer farms where it is more profitable to continuously and rapidly create addresses and checking their balance in hopes of someone out there sharing it?

Or will the amount of power usage generated from such an idea be more profitable simply going to mining?

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I think the way to reason about this is to think about the incentives and rewards of such actions.

Yes, I can potentially throw a lot of computational work into generating private keys and checking their balance... But is it really worth it knowing that I can throw the same amount of energy into Mining, and get a guaranteed and constant return on my computational work?

Somebody was discussing something similar in 2012 on BitcoinTalk, here's the link https://bitcointalk.org/index.php?topic=107172.0. Note that the author of the post says that "you probably have much better odds finding extraterrestrial life or winning the Powerball 5 times in a row" than randomly finding a generated BTC address with a balance in it.

EDIT: Reason for the downvotes? Why did a couple of people damage my account reputation without explaining exactly what is wrong with my answer? So sad this community is not as nice and newbie-friendly as it should be.

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    This does not accurately describe the impossibility of generating the same key that has been used before, which is almost zero chance. – Anonymous Sep 29 '19 at 16:10
  • Why you downvoted me? :( I don't think I've said anything wrong! I answered questions from OP in a simple way and pointed to another relevant discussion on bitcointalk. Why did you just pass by here to damage my account, critique me with the generic comment "which is almost zero chance" and not leave any other meaningful contribution? I understand you are a super smart developer, but it's not a reason to be so salty towards a more simple answer like mine. Hostile people like you are what slows down the growth of the crypto community, especially when it comes to helping each other. Disappointed – bitfede Sep 29 '19 at 16:28
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    @bitfede welcome to Bitcoin.SE! People here are generally friendly, don’t read into a single downvote so heavily. I agree your answer is not incorrect, but it also does not provide any explanation of ‘why’, except in the link you posted. Since links can break over time, it is preferable to post the relevant info in the answer itself, even if you just quote from the link. – chytrik Sep 29 '19 at 19:17
  • Hey @chytrik thank you for your reply and for the explanation. Will keep all this in mind. – bitfede Sep 29 '19 at 19:26
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    I'll have to upvote you when I have the rep, @bitfede. I asked because I recently wrote a simple dictionary attack to bitaddress.org's brain wallet function and I came across a decent amount of addresses with balances on them. Yes, I understand that this was exploiting the human aspect of key from password creation, rather than bitcoin's digital signature algorithm, but I was curious to the mathematical probability of brute force create and check compared with the amount of addresses already created along with the creation rate and if it could ever be theoretically plausible. – Amit Yehuda Sep 29 '19 at 22:52

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