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I'm sure that this question has been asked before, but I just can't seem to find it.

If there is a limit of 21 million coins to be mined, then what happens if Bitcoin wallets get deleted? Will there still be some percentage of mining that occurs to make up for the lost coins?

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If Bitcoin wallets get deleted, lost, or otherwise inaccessible, then the Bitcoins contained in them cannot be accessed anymore. There is no compensation for these "lost" Coins, and it is hard to see how there could be any such compensation. After all, nobody can prove that they lost some data. Hence any compensation scheme would likely be open to fraud.

As a consequence, Bitcoin has been called deflationary because presumably some such loss of Bitcoins will always happen. However, this does not mean that there will not be any mining after all Bitcoins have been created. Mining is driven by two kinds of rewards for the miners, the new Bitcoins (which will cease at some point) and the transaction fees that get transferred from the senders to the miners. Whilst usually it currently works just fine to send not-too-small transactions with zero fees, including one might just speed up transactions, so Bitcoin users actually have some (albeit possibly small) incentive to offer the miners a reward for their activity.

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Sadly, lost Bitcoins are lost... never to be re-incarnated.

That said, your (non-lost) bitcoins should rise in value because of such loss occurring over time.

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As @pyramids and @john-devor explained, as it stands today, the bitcoin mining rules will not make up for any lost bitcoins. So in theory the total amount of bitcoins in circulation will never reach the full amount initially defined by the protocol.

If you think about it, it's very difficult to identify "lost" coins. Just because a wallet is not touched in years, it doesn't necessarily mean the private key was lost (as likely as it may appear).

Having said that, Bitcoin is only sofware, and that software can be modified in the future.

If somewhere down the line people find that there aren't enough bitcoins to serve the global economy (remember that most people will not be trading BTCs but mBTCs or uBTCs, etc) nothing is stopping the community and developers from agreeing on a new ceiling and implementing that in a future version of all bitcoin clients, effectively making more coins available for mining.

It would be a tricky change from a socio-economic perspective, because it would have a significant impact on the value of the existing coins, but it is possible.

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The other answers are only partially correct. BitCoin uses ECDSA keys to secure wallets. Your public address is simply the public key of the keypair, and your "wallet" has the private key for each public address (note: it doesn't show you this key as too many people would do foolish things with it). Currently there's no practical means to reverse a public key to find the private. So coins secured by a lost private key (lost the wallet or otherwise) are inaccessible.

However, ECDSA is susceptible to Shor's algorithm. Quantum processors are limited to 4-qubits, last I looked, so BitCoin's 256-bit keys are safe for the time being. Eventually Quantum Processors will get to the point where they can crack 256-bit ECDSA. Just before that happens BitCoin has a built-in mechanism to announce the use of a new address algorithm, everyone starts using that and life is good still. Just after those processors are available someone will undoubtedly use them to crack the wallets which have not been upgraded and grab the BitCoins, returning them to circulation.

I'm not sure if this was an intended "feature" of BitCoin. ECDSA was the best we had (still the best of the well cryptanalyed algorithms, as of writing), but we've known for some time that someday quantum processors would make it obsolete. In any case it's likely that 256-qubit processors will not be available for a decade, possibly more, so nothing to worry about for a while.

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