Lost bitcoins won't be recovered without access to lost private keys. It's impossible as from Private key to Public key then public address is one-way. You can not revert the process from Public address to Public key then Private key.
Not at the moment, but reversing a public key to a private key could certainly be possible far enough in the future with quantum computers. If such an event occurred, then the several million coins in early P2PK outputs as well as any coins in outputs with a revealed public key (which includes all addresses which have previously spent bitcoin) could potentially have their private keys reverse engineered and therefore re-enter circulation, unless the community consensus is to fork to somehow lock all these coins.
Just because coins have not moved in a long time, or even if someone claims they have lost the private keys/seed phrase/wallet/whatever, it is wrong to assume those coins are permanently lost and can't be recovered.
However, you won't be able to know how many bitcoins were lost.
We can prove that the number of provably lost bitcoin is 2,828.654 BTC, and this number can be safely removed from both the total and the circulating supplies. Anything which is not provably lost should not be considered removed from the supply.
@o_e_l_e_o I have read your comment with great interest as it is a question that I often ask myself and research it from time to time for new information.
When you say that the reversal of a public key to a private key could
certainly be possible at some point in time in the future, wouldn't that be the end of Bitcoin entirely? You are now talking about specific outputs, but wouldn't that possibility for reversal apply to any known public key? How would Bitcoin survive such an event anyway?
I think I am probably not sufficiently understanding the mechanics and the consequences, but isn't a potential recovery of
now so called permanently lost Bitcoin equal to Bitcoin's algorithm being cracked?
I would also like to ask you where you got the number
2,828.654 BTC from? You have given some answers here to some research that I am into from time to time and perhaps you can elaborate or provide a source.
Many thanks in advance!