Estimates have been thrown around a lot recently as to the year in which the last Bitcoin will be mined- where are these estimates coming from? Could someone send me to the relevant code?
The estimate is 2140 based on the block reward halving frequency of four years. According to math and knowledge that there are 32 halving events, in 2136, the block reward will yield 0.00000168 BTC per day, which is 0.00000042 BTC per block. That's 42 satoshis.
It's arguable that there could be one additional halving, to a block reward of 0.00000021 BTC, but that would require a major protocol modification since the number of Bitcoin would then exceed 21 million. Additionally, to go past that, there'd have to be a protocol modification to extend divisibility past eight decimal places. It is far, far to early to worry about either of these, because we're more than a century away from this problem.
Under the assumption that halvings will occur every four years, the final block that creates new bitcoins would occur in 2140.
The "halving" occurring with block 6,930,000 would then push the reward below 1 satoshi, thus no block reward would be paid out anymore.
You can find a table with the respective calculations here: Bitcoin Reward Schedule
Really, the mining reward might be too little to pay for mining efforts much earlier: already in 2036 99% of the bitcoins will be in circulation, in 2048 it will be 99.9%.