Why 21 million Bitcoin?

Did you know that the maximum number of 21,000,000 BTC is actually not correct? In this short article, I would like to show you how many Bitcoins - or rather how many Satoshi (the smallest unit of a Bitcoin) - there will ultimately be.

At some point in the course of your life as a bitcoiner, you come to the point where you ask yourself the question: Why exactly 21 million? Why not 20, 25 or even 100 million? How does this number come about?

Well, opinions differ on this question, because Satoshi Nakamoto himself never gave a clear answer to this question. Some people think that the amount of Bitcoin was chosen so that if the entire money supply in the world were represented in Bitcoin, 1 cent would be approximately 1 Satoshi. However, most people simply believe in a certain arbitrariness that goes hand in hand with the fact that Satoshi wanted to set the average block time at 10 minutes and that the so-called block subsidy should halve approximately every 4 years.
Coupled with an (equally arbitrary?) initial reward of 50 BTC per new block, this results in a limit of 21 million BTC.

Let's do some math 🙂

6 blocks per hour x 24 hours per day x 365 days x 4 years = 210,240 blocks per cycle.

However, as Nakamoto did not want to choose such a "crooked" number for the cycle, he rounded it down to 210,000 blocks (according to theory).

The sum of all block subsidies at infinity is: 50 + 25 +12.5 + 6.25 +3.125 + .... = 100

In theory, we therefore actually arrive at :

210,000 blocks x 100 BTC = 21,000,000 BTC

However, there is a problem. And that is the Bitcoin protocol itself. It only defines eight decimal places for Bitcoin. If halving the block subsidy results in the new subsidy having more than these eight decimal places, everything from the ninth place onwards is simply cut off, according to the Bitcoin source code.

This leads us to the following result:

21 million? No!

As you can see, Bitcoin already reaches its maximum limit at 20,999,999.97690000 BTC.
Strictly speaking, you should not say "there will be 21 million Bitcoins", but rather :

"There will be a maximum of 2,099,999,997,690,000 Satoshi ".

Since it probably takes a little too long each time

"Two quadrillion, ninety-nine trillion, nine hundred and ninety-nine billion, nine hundred and ninety-seven million and six hundred and ninety-thousand satoshi"

it's probably better to just keep saying:

"There will be FAST 21 million Bitcoins".

Some interesting facts for you

  • What the table above also shows wonderfully is the fact that more than half of all possible Bitcoin has already been created by the first halving on November 28, 2012.
  • Incidentally, the first time that a decimal place has to be cut off will be at the tenth halving, when the block subsidy "halves" from 0.09765625 to just 0.04882812.
  • The last whole Bitcoin will be mined in the sixth era around 2032.
  • The last Satoshi will be mined in the 33rd era, around 2140.
  • In the last 30 years between 2110 and 2140, not even one whole Bitcoin will be mined in total.

What do you think? Did Satoshi have something in mind when he chose the parameters so that just under 21 million BTC would be the final number? Or was it just a coincidence? Feel free to write your opinion in our forum.blocktrainer.de