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Why did Satoshi pick 21 million as the number of bitcoins to be created? What is the significance of that number?

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I thought this question had already been asked, but I can't find it. –  Lohoris Mar 17 '13 at 15:59
I added the finance tag since this question is asking about not just the math behind how 21 million blocks was created, but the reasoning behind all that math from an economic perspective (assuming there was one) –  makerofthings7 Mar 18 '13 at 5:31
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6 Answers

up vote 30 down vote accepted

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.

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Good explanation, but you're just postponing the answer. Why 4 years per cycle? Why was 4 years per cycle picked as the number for years per cycle? –  Andrei Mar 17 '13 at 17:41
All this info makes sense, but doesn't really answer the question! –  B Seven Mar 17 '13 at 18:29
If you check my original answer, you'll see I ended with "but I don't know the economics behind it". I see that has since been edited - not by me. –  Chris Moore Mar 17 '13 at 21:24
Interesting. Does this mean that slightly more than 21 million bitcoins will be created? –  Nick ODell Mar 17 '13 at 21:39
No, slightly less than 21 million, because of the rounding error on the last halvings. –  Andrei Mar 17 '13 at 21:42
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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 intererest 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 the 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.

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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.

  1. New Bitcoins enter the system in an orderly, predicable way.
  2. Outside forces cannot arbitrarily flood the currency with new money.
  3. An incentive is provided for people to apply their CPU power to make the currency more secure.
  4. 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.

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I can offer another explanation why Satoshi picked 21 million as final number of bitcoins. As it is not so imporatant 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.

Since Bitcoin is often compared to gold, total number of Bitcoins matches total amount of gold mined in human history which can be imagined as a cube 21 m on a side.

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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.

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This was done based on production rate mostly. They did take some things into account but the number doesn't have a real economical explanation rather than the fact that they had to stop production somewhere to maintain a value.

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