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I know its extremely unlikely, but considering creating wallets is free, and the fact that Bitcoin will hopefully still be a thing centuries and even milleniums from now, with time it will become more probable.

what would happen if two people created a wallet with the exact same key?

They would have generates the same wallet and thus could steal each other's funds for example.

with time it will become more probable

Yes but still negligible

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So, in theory, to avoid this you would have to use a BIP 39 passphrase, right?

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150 sats \ 0 replies \ @ek 5 Jun 2023

Kind of. You would make it harder to accidentally generate the same wallet.

But honestly, don't worry about it.

The chance to generate the same seed by accident is 1 divided by 2048^n where n is the amount of words you use since BIP39 has 2048 available words. [0]

So for example, if you use 24 words, it's once every 2048^12 = 2^11^24 = 2^264 attempts which is between 10^79 and 10^80.

For comparison, it is estimated that there are between 10^78 to 10^82 atoms in the known, observable universe. [1]

[0] https://github.com/bitcoin/bips/blob/master/bip-0039/english.txt#L2048 [1] https://www.universetoday.com/36302/atoms-in-the-universe/

Does that convince you to no worry about it?

Or at least convince you that this is not the use case for BIP 39 passphrases. Afaik, it's only meant for hidden/decoy wallets or for additional security in case someone finds your seed phrase.

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That would never happen, right? Unless ...

https://bitcoin.org/en/alert/2013-08-11-android

https://bravenewcoin.com/insights/blockchain-info-bug-exposes-users-private-keys

https://medium.com/mycrypto/disclosure-key-generation-vulnerability-found-on-walletgenerator-net-potentially-malicious-3d8936485961

and those are just a few examples.

That is why for large amounts of value, ... rolling dice, and other similar methods for obtaining a private key is not necessarily unwaranted.

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To give you an idea of scale of numbers involved: http://miguelmoreno.net/wp-content/uploads/2013/05/fYFBsqp.jpg

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