The 21,000,000th bitcoin will never be reached.
It takes
4 years to go to 10,500,000
8 years to go to 10,500,000+5,250,000
12 years to go up to 10,500,000+5,250,000+2,625,000
16 years to go up to 10,500,000+5,250,000+2,625,000+1,312,500
etc...
It takes
4 years to go to 10,500,000
8 years to go to 10,500,000+5,250,000
12 years to go up to 10,500,000+5,250,000+2,625,000
16 years to go up to 10,500,000+5,250,000+2,625,000+1,312,500
etc...
I hope that this is just a joke referencing zeno's paradox
No it is not a joke. Due to limited significant digits the subsidy will reach 0.00000000 BTC before 21M BTC is reached.
On the 33rd subsidy cut the subsidy will be exactly 0 (and will remain 0 for all future blocks) and 2,099,999,997,795,000 satoshis (20,999,999.97795 M BTC) will have been minted. That is 2,205,000 satoshi's (~0.02 BTC) short of 21M BTC. If the number of decimal places was increased more coins would be minted but still be short of 21M.
So it is more accurate to say "no more than 21 million BTC will be minted".
Satoshi could have avoided this by working backwards when designing the subsidy. Design the last block reward and then double it working backwards to get the initial block reward (which would be a power of 2). Then the sum of coins would be exact. It doesn't really matter but it is one of those minor annoyances that just bug me.
Ah, thanks for that. I had been under the (mistaken) impression that it was infact calculated to mine out exactly 21M by the 22nd century and then once exhausted switch over to transaction fees. That does seem a bit inelegant.
