Why did Satoshi pick 21 million as the number of bitcoins to be created? What is the significance of that number?
Here's a mathematical explanation:
Calculate the number of blocks per 4 year cycle:
6 blocks per hour * 24 hours per day * 365 days per year * 4 years per cycle = 210,240 ~= 210,000
Sum all the block reward sizes:
50 + 25 + 12.5 + 6.25 + 3.125 + ... = 100
Multiply the two:
210,000 * 100 = 21 million.
Economically, because the currency is effectively infinitely divisible, then the precise amount doesn't matter, as long as the limit remains fixed.
I don't know if this was thought up ahead of time, but it sure makes sense in hindsight.
The reason 21 million is the right number is because people don't know how to value currencies.
For instance, right now a Euro is worth $1.30 USD and a Japanese yen is worth about a U.S. penny. Ask someone which currency they would rather hold right now and most will answer Euro, because $1.30 is worth more than $0.01.
Of course, that relative unit value means nothing. Ask most currency traders which currency is better to hold and most (today) would probably say Japanese yen, because what matters is whether the value will go up or down, relative to the other being compared.
When bitcoin hit parity with the U.S. dollar in Feb 2011, it gained a sense of legitimacy that helped propel it on a tremendous pace, rising over 30X that level just four months later.
If there had been more than 6 million coins issued by then, the total dollar value of all bitoins would probably have been about the same, and thus the exchange rate would then have been lower. So let's say there were instead 60 million coins issued by Feb 2011, and each one worth a dime. That 60M X $0.10 is the exact same total dollar valuation the 6M X $1 has ($6M) for all bitcoins combined. Tthe difference is that because it had become "worth more than a dollar", and as a result people attributed greater interest and respect for it. Had it not been "worth more than a dollar" so early, it might have taken a whole lot longer to get the name recognition and attention it did that has helped attract the participants that Bitcoin has today.
Bitcoin today stands on "dollar parity"'s shoulders.
That may sound bizarre but ask that Euro / Yen question to different people yourself and then ask the reason why their answer was given.
So the number needed to be a low enough number so that while total dollar valuation of all bitcoins was still in the single-digit millions it would reach parity with the U.S. dollar at some point.
A total of 174,100 tonnes of gold have been mined in human history, according to GFMS as of 2012.2 This is roughly equivalent to 5.6 billion troy ounces or, in terms of volume, about 9261 m3, or a cube 21.0 m on a side.
Since Bitcoin is often compared to gold, the total number of bitcoins matches the total amount of gold mined in human history which can be imagined as a cube 21 m on a side.
As it is not entirely so important how many Bitcoins will exactly be mined. Satoshi could have easily chosen almost any number. He could just adjust block reward halving (210 000 blocks), reward sizes (50, 25, 12.5 ...), etc. to match some particular number.
Satoshi Nakamoto himself compared Bitcoin to gold.
As a thought experiment, imagine there was a base metal as scarce as gold but with the following properties:
- boring grey in colour
- not a good conductor of electricity
- not particularly strong, but not ductile or easily malleable either
- not useful for any practical or ornamental purpose
and one special, magical property:
- can be transported over a communications channel
The exact number of Bitcoins is not important. Whether the end result is 1 million or 100 billion makes little real difference.
The important aspect here is the process, not the quantity.
- New Bitcoins enter the system in an orderly, predicable way.
- Outside forces cannot arbitrarily flood the currency with new money.
- An incentive is provided for people to apply their CPU power to make the currency more secure.
- Eventually, Bitcoin has to be self-supporting through transaction fees. Hence the tapering off of blockchain rewards.
Having said all that, there are some psychological advantages to having a low limit like 21 million. It was inevitable that people would see Bitcoin as being "more valuable" if the exchange rate for a whole Bitcoin was over $1. Ensuring this "high exchange rate" but making the coins highly divisible was probably a conscious design decision.
It is the result of a 50 bitcoin reward half life of 210,000 blocks.
Reward starts out at 50 bitcoins and halves ever 210,000 blocks. This works out to be 2.1 quadrillion monetary units of currency (satoshi). This is probably the largest number estimated to be needed for a global currency and some padding for attrition.
I suspect it has something to do with the M1 USD supply at the time Satoshi was developing Bitcoin. If you look at the decade prior to the white paper, inclusive of the quantitative easing period commencing with the 2008 housing bubble, the M1 money supply shows a trendline with a slope of ~58, using years as 4 digit integers. This means, that if predicting M1 over the next decade (from 2009 to 2019), there would be an expected M1 of 2.1 trillion USD, at which point 90% of all bitcoin will have been mined. Because Bitcoin is designed with an 8 decimal fraction system, the 21 million total BTC can actually be expressed as 21,000,000.00M = 21,000.00Billion = 21.00Trillion. So roughly 9x functional BTC will exist relative the USD. Using the M1 trendline to predict M1 in 2140, we see an expected ~10Trillion, which relative to the 21Trillion functional BTC, still gives us a 2x cushion on volume. And mathematically, we've seen noted elsewhere in this Q&A that the 4 year halving schedule of the coinbase gives us 21Million BTC. So, there's a convenient convergence of predicted volume needs & reward schedule @ 21Million BTC. (But realistically, this is probably just me seeing signal where I want to see signal, and not actually Satoshi's anticipation of volume.)
I think another curious question is why the 4 year halving schedule? Is this based on national US elections? Is it based on a calendar Leap Year? Is it Satoshi's approximation of a reasonable re-evaluation period for BTC participation rates?
Very simple answer: The reward for Bitcoin Miners had been 50 Bitcoins per Block for the first 210,000 Blocks. For the next 210,000 blocks it is the half of 50 (=25). Take the geometric series and you'll be getting the total amount of nearly 21 Million Bitcoins (nearly, because a geometric series converges to his boundary value, but never reaches it!).