According to various estimates, at least 4 million coins were lost by users, but they were mined by miners and put into circulation. And some of them may even be found someday. Someone will find their old HDD or stumble upon notes in a notebook with a long-lost seed-phrase (I do not recommend storing your seed-phrase this way). But will the entire supply of bitcoin be exactly 21 million in the end?
Let's find out.
First, let's get back to the Bitcoin halvings. We know that every 210,000 blocks (~4 years) the reward for miners is halved. And we also know that one bitcoin can be divided into 100,000,000 sats. These are our initial conditions, which are set in stone of the network. If we start dividing the initial reward of 50 BTC (5,000,000,000 sats) in half, then on block number 2,100,000, which will be mined around April 2048, it turns out that the reward will decrease to 4,882,812.5 sats. But we can't split 1 Satoshi in half, so the network will start rounding the reward down. Thus, the block reward will be 4,882,812. This situation will repeat itself over and over again.
Based on this information, we can calculate that in block 6,929,999 mined in ~February 2140, the total emission will be 20,999,999.9769 bitcoins. Right? No!
The Bitcoin consensus rules say that the maximum reward for miners per block cannot be increased. It is mandated by the halvings and will only decrease over time. BUT the consensus rules do not prohibit miners from lowering their block rewards. You may say: "who in their right mind would lower their reward?" But, as it turned out, there are several known cases associated with this... feature?
On June 8, 2011, a BitcoinTalk forum user with the nickname midnightmagic wrote that when he mined block number 124724, he lowered his reward by exactly 1 satoshi, thereby expressing his grief at the then disappearance of the creator of bitcoin.
“I did it as a tribute to our missing Satoshi: we are missing Satoshi, and now the blockchain is missing 1 Satoshi too, for all time.”he said.
You can find block number 124724 in any block explorer and clearly see that it actually generated not 50, but 49.99999999 BTC. Thus, this 1 Satoshi disappeared forever, or rather, did not even appear.
In addition, it is known that the miners who mined blocks 501726 and 526591 did not receive, or did not fully receive the reward, which at that time was 12.5 BTC. The miner who mined block 501726 did not receive a block reward for some reason, which caused an error in some block explorers. On the block page in blockchain.com, the address of the miner who mined this block is not indicated at all, and the earned commissions indicate the simply impossible amount of 184467440724.5955 (184+ billion) BTC. Perhaps he was trying to use custom software that had bugs, or idk. It's hard to say exactly, and the information is varies source to source. In turn, the miner who mined block 526591 most likely lowered his own reward (6.25 instead of 12.5). The motive for this action is also not known for sure.
The chance that such cases will repeat before 2140 is high. Because of them alone, 18.75000001 BTC are permanently deducted from the total supply. Is it bad? No, because bitcoin has become even more scarce!
As a result, we can say that at the moment the total emission of bitcoin is no more than 20,999,981.22689999 units.

What do you think about this?

Let me know in the comments if you have any additional information about this cases or any new ones. Thanks! P.S. sorry for poor english and typos.
In fact on this page you can see the amount of supply that there is currently, and see all the blocks that for some reason failed. https://bitcoin-supply.com/
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It really depends if we die and on how our children's children view Bitcoin. It's code, it's an explanation of an voluntary economic system, literally any part of it is subject to change given adequate reason. Never is only useful for physically impossible things, like light going faster than the speed of light. It is possible that code changes, for example, give satoshi's coins to miners as the block reward starts to decline for some security related reason and enough people in a hundred years agree to run the software. I'm not saying it's going to happen, I'm just saying that it's not outside of the realm of being a solution to some problem in a future which has infinite unknown problems.
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I think lost coins should stay as it is. Any changes in the code for returning some of the lost coins will have a lot of consequences. What if they’re not lost? What if after that we will decide to “find” other peoples coins too? Should we rely on people's honesty again? I think we shouldn’t. Lost means lost. Period. If we’re gonna lost 90% of it — okay. Let it be. No more fiat money.
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Nice write up. It's also interesting to think of bitcoin is deflationary, because inevitable more people will lose their coins. People passing away without setting up some kind of beneficiary, forgetting seed phrases, etc. are all inevitable.
My guess: ♾/14 million in 2140 (1 million being Satoshi Nakamoto's)
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Very interesting. Some fascinating details i wasn't aware of. They could probably do a BIP to make it exact when we get there. I hope I'm still around to see that glorious day. Thankyou.
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Here's some math:
Calculate the supply of bitcoin: Σ[(100/(2^n)) x 210,000] = (50 x 210,000) + (25 x 210,000) + (12.5 x 210,000) + ... + (0.00000001 x 210,000) = 20999999.99755528 limit (epochs) = 33 n0 = 1
Calculate the max possible supply at a block height: Number of epochs = current block height / 210,000 e.g. block height = 750,000, therefore 750,000/210000 = 3.57 750000 - (3 x 210,000) = 120,000 blocks into 4th epoch (50 x 210,000) + (25 x 210,000) + (12.5 x 210,000) + (6.25 x 120,000) = 19,125,000 bitcoin could have been minted.
Verify the actual number of minted bitcoin: Using a full node (e.g. Bitcoin Core), run the RPC command 'gettxoutsetinfo'. On a RasPi this may take a few minutes to compute. The 'Total Amount' value is the actual number of minted bitcoin.
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Can you run the 'gettxoutsetinfo' command and text me how much it shows?
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Check out this podcast we made discussing the total amount of bitcoin. Your are right, there will never be 21M but close to it:
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Don't forget that the initial 50 from the genesis block is unspendable. Though, I suppose a hard fork permitting that could occur, I suppose. Probably not a priority for Satoshi to be able to spend 50 of the one million coins attributed to mining by Satoshi.
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Intriguing, how come that 1 sat disappeared? That goes against the core platform of bitcoin right, that everything is 100% trackable forever by everyone.
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Now though, you can't lower your reward.. It has to be the exact block reward, or your block will be considered invalid.But even if you follow the issuance correctly and would have collected all the rewards, you still will never get a total of 21 million btc ever, because the first blocks 50 btc coinbase can never be spent. There is a really good SO answer about this, can't find it right now.
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I was aware of most of these incidents, but this is a nice writeup, good job.
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