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Hi is there a database of wallet addresses that have lost the private keys?

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No, because it's not possible to prove a negative ("No I don't have the private key for that address") and I can't think of a use for that.

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Not really, it's not possible to be sure that the private key corresponding to a given address is lost.

However, it's possible to find in the blockchain addresses that have coins in them and haven't been used for years. This might indicate that original owner has lost access to this address. It doesn't mean that it won't be reclaimed, either by the same person or someone else gaining access to the keys, e.g. by data recovery from an old hard drive or, in the future, speculatively, by breaking the cryptography used to secure Bitcoin. However, it might not be lost at all, it might be used as long term storage.

For examples of such addresses you can check this list, which collects 100 richest addresses that hasn't been spent from for 5 years. The same website also has lists for up to 8 years of dormancy.

Moreover, there are addresses used for intentional burning of Bitcoin, such as 1CounterpartyXXXXXXXXXXXXXXXUWLpVr. In this case, it is certain that the address doesn't have any private key corresponding to it, because generating such a private key isn't computationally feasible. It is a special case, however, because in this case the key wasn't lost, it was never generated.

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