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After the 21 millionth bitcoin or 20 999 999th bitcoin is mined, what will happen to bitcoin mining? - will it just stop, or will we make a further division of the satoshi thanks to Bitcoin's infinite divisibility? Or maybe miners could mine a share of the Bitcoin transaction fee...

Any suggestions/mathematical answers are appreciated.

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You assume this moment will happen. I'd say economically adjusted cryptocurrencies (if not new and completely different versions of Bitcoin) will spring up, and make the current scheme obsolete long before this moment were to happen. Just sayin'... –  Stéphane Gimenez Nov 6 '12 at 23:54
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Technically, I think you are missing a few decimals. There's still many years between 20,999,999 and 20,999,999.99999999 or whatever point the very last satoshi is mined. As far as currency inflation goes though, the block reward stops having an effect long before the 20.9 million range. –  Stephen Gornick Nov 7 '12 at 3:31

4 Answers 4

up vote 10 down vote accepted

Assuming Bitcoin is still active at that point in time, mining will continue, because transaction fees will make it worthwhile to do so.

This topic has been discussed heavily in other answers, including:

The last link has suggestions that the fee mechanism of Bitcoin may need changing, though that's yet to be proven whether or not it will be a real problem.

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I downvoted because market-based transaction fees don't scale. I read that even Gavin has expressed his doubt that they will. –  Shelby Moore III Mar 28 '13 at 1:43
    
@ShelbyMooreIII, you're assuming we try to scale up with the current implementation, which is not a realistic assumption. I'm working on the assumption that the client and/or protocol will adapt as necessary, which is clearly in progress. If the next phase of adaptations don't resolve the issues, then there will be another phase. –  Highly Irregular Mar 28 '13 at 2:53
    
You are willing to risk giving the monopolists the 51% attack because you assume you can make tx fees scale later? Fishing w/o fuel to return? Very responsible given humanity's future hangs in balance. Readers should click to my activity, read many comments of mine to get some context for this comment. Highly Irregular & I have been trading comments else where today. Soon it will be too late for phases. Bitcon will have enough mcap for the monopolists to take over mining and run with it from there as bastardized vision of what you wanted. You will then cry while mankind is enslaved. Good job! –  Shelby Moore III Mar 28 '13 at 3:35
    
@ShelbyMooreIII, ok, so now you're raising a different concern: that corporations will gain control over the majority of the hashing power. I also have that concern because of the massive hardware requirements a Bitcoin node is likely to require in future, but it needs addressing in a completely separately question that's focused on that problem. –  Highly Irregular Mar 28 '13 at 4:39
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Why can't you see the two concerns are mutually dependent, not separable? Without scalable tx fees, you must have monopolization, else you don't scale and crash and burn (at least in terms of the expectations of the investors). The key issue is always profitability which makes the two inseparable. You see what I mean by people can't assimilate facts as well as I can? –  Shelby Moore III Mar 28 '13 at 5:16

Every block has exactly one "coinbase transaction", the one transaction which doesn't have actual inputs, but gets all the fees and mining subsidy.

Every 210000 blocks, this subsidy halves. Right now, each block is allowed (not required!) to bring 50.00000000 BTC into circulation. Very soon, this will become 25.00000000. Four years later, 12.50000000. And this will continue: 6.25, 3.125, 1.5625, and so on. There are only 8 decimals though, and at some point the subsidy will only be 0.00000001. Four years after that, it will effectively become zero. This will not happen this century, though.

This doesn't mean that there won't be any blocks produced anymore. Assuming Bitcoin is still alive, we'll still have blocks being produced every 10 minutes. Miners will just get all their income from fees, without any subsidy.

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The short anwser is that miners will rely on transaction fees, to get paid.

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I downvoted because market-based transaction fees don't scale. I read that even Gavin has expressed his doubt that they will. –  Shelby Moore III Mar 28 '13 at 1:42

I have read that the expanded use of cryptos will possibly (likely?) overtake credit/debit card transfers. Assuming BTC is the one that does this, simply a .1% share of the world economy would make each bitcoin worth $38,000 (don't slay the messenger, I'm going from memory) and fees that were capped at 1% would probably make the block rewards pale by comparison. As for the hardware requirements, huge database requirements could be eliminated by blockchain "PRUNING" which would shorten the blockchain.

Good answers above, I just wanted to add this as pertinent.

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