Here's a very interesting thought against the depletion of btc.

25 millionbtc exist to be mined if weve mined about 1m and all the companies and/or banks get in on this. Wont it mean we will run out of btc a lot faster then the predicted 2020-2040(which I believe it may be shorter than that)

Theories?

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Yes, it will be sooner than originally predicted(to reach 21 million). The problem is hashpower gets added after the calculation is made each time at the 2016 block mark. That's why we are ahead of schedule and it takes less than 14 days most of the time to reach 2016 blocks.

Note: It isn't so much that the amount of hashrate added is excessive (although there is a limit to how much the difficulty can increase - 400% every 2016 blocks), it is that the additional hashrate is not all added at the same time. Say for example that when the difficulty changes, exactly 10% additional hashrate is added to the network then at 1008 blocks after the difficulty changes, an additional 10% of hashpower is added to the network (off of the original hashrate) (and no variances in luck and no other changes to mining power) then by 2016 blocks after the previous difficulty change, the difficulty will be 15% higher but the hashrate will be 20% higher.

This is the block chain's control theory feedback loop:

60minhr∗24hrday∗7dayweek 10minblock=2016 in 2weeks

Tcurrent=Tprior∗tprior/2weeks

D=work/2(32)=2(256)/(Tcurrent+1)∗2(32)

hashes/second≈D∗2(32)/600

The current target for the block chain is determined by a calculation, so any two clients looking at the block chain will calculate the same target. This calculation aims to adjust the target such that one block will be mined every 10 minutes, no matter how much total computing power is devoted to mining. The target changes every 2016 blocks based on the timestamps within those blocks. Why 2016? Because Satoshi decided two weeks was a good interval, and at 10 minutes per block, 2016 blocks will be mined every two weeks.

When 2016 blocks take more than two weeks to mine, the target goes up to make mining easier; when they take less than two weeks, the target goes down to make mining harder. In symbols, if Tprior is the previous target and tprior is the time it took to mine 2016 blocks using that target, then the updated target Tcurrent is just.

The target is typically a huge number well in excess of 2(200). Also it goes down as the total hashing power of the miners goes up. Consequently, interested people usually think in terms of the difficulty instead. Definition: The Bitcoin difficulty is the average number of nonces you have to try to find a valid block — aka. the work — divided by 2(32)(roughly 4 billion).

Note that D is just a number for human consumption. It scales in direct proportion to the computational effort required for mining, so twice the difficulty means twice the effort.

If we know the current difficulty D, we can estimate how fast all miners are hashing in aggregate. On average, it takes D∗2(32) hashes to find a nonce that works, and the target is selected to make that take 10 minutes.