Why was 21 million coins chose as the total number of bitcoins?

[DannyHamilton]

21 million was the intended number, it isn't "derived" in the sense that it's an arbitrary number.  It was coded intentionally to produce 21 million.

Really?

Did you have a conversation with Mr. Nakamoto whereby he explained this to you?  Or are you just making things up out of your own imagination and assuming that you are correct?

If he wanted to produce exactly 21 million then he did a poor job of programming.

There will never be 21 million bitcoins.  The maximum that will be produced with the programming that Mr. Nakamoto chose is: 20999999.9769

If he was specifically intending 21 million, then why would he code it to intentionally produce only 20999999.9769?

[ngocbkcse]

this is the 21st century --> 21M BTC

[GreekBitcoin]

So that if all gold speculation goes to Bitcoin (at the prices of 2009) the price of bitcoin would be 1000000$

[runpaint]

21 million was the intended number, it isn't "derived" in the sense that it's an arbitrary number.  It was coded intentionally to produce 21 million.

Really?

Did you have a conversation with Mr. Nakamoto whereby he explained this to you?

No, Hal Finney and Ray Dillenger did.

Ray Dillenger recalls:

I remember this discussion, actually.

Finney, Satoshi, and I discussed how divisible a Bitcoin ought to be.  Satoshi had already more or less decided on a 50-coin per block payout with halving every so often to add up to a 21M coin supply.  Finney made the point that people should never need any currency division smaller than a US penny, and then somebody (I forget who) consulted some oracle somewhere like maybe Wikipedia and figured out what the entire world’s M1 money supply at that time was.

We debated for a while about which measure of money Bitcoin most closely approximated; but M2, M3, and so on are all for debt-based currencies, so I agreed with Finney that M1 was probably the best measure.

21Million, times 10^8 subdivisions, meant that even if the whole word’s money supply were replaced by the 21 million bitcoins the smallest unit (we weren’t calling them Satoshis yet)  would still be worth a bit less than a penny, so no matter what happened — even if the entire economy of planet earth were measured in Bitcoin — it would never inconvenience people by being too large a unit for convenience.

https://thewealthofchips.wordpress.com/2014/10/01/why-bitcoin-is-and-isnt-ideal-money/

Danny Hamilton, you're not smart enough or important enough to back up how much of an asshole you are.  Maybe take it down a few notches, especially when you're wrong and making a fool of yourself.

[R2D221]

I think asking this kind of questions is like asking “Why did you wear green clothes today?”. Yes, there was a decision to be made, but not a very deep one, to be honest.

[runpaint]

I think asking this kind of questions is like asking “Why did you wear green clothes today?”. Yes, there was a decision to be made, but not a very deep one, to be honest.

Except you're wrong, as shown by the above quote regarding the decisions that went into determining the supply of bitcoins.

[DannyHamilton]

21 million was the intended number, it isn't "derived" in the sense that it's an arbitrary number.  It was coded intentionally to produce 21 million.

Really?

Did you have a conversation with Mr. Nakamoto whereby he explained this to you?

No, Hal Finney and Ray Dillenger did.

Ray Dillenger recalls:

I remember this discussion, actually.

Finney, Satoshi, and I discussed how divisible a Bitcoin ought to be.  Satoshi had already more or less decided on a 50-coin per block payout with halving every so often to add up to a 21M coin supply.  Finney made the point that people should never need any currency division smaller than a US penny, and then somebody (I forget who) consulted some oracle somewhere like maybe Wikipedia and figured out what the entire world’s M1 money supply at that time was.

We debated for a while about which measure of money Bitcoin most closely approximated; but M2, M3, and so on are all for debt-based currencies, so I agreed with Finney that M1 was probably the best measure.

21Million, times 10^8 subdivisions, meant that even if the whole word’s money supply were replaced by the 21 million bitcoins the smallest unit (we weren’t calling them Satoshis yet)  would still be worth a bit less than a penny, so no matter what happened — even if the entire economy of planet earth were measured in Bitcoin — it would never inconvenience people by being too large a unit for convenience.

https://thewealthofchips.wordpress.com/2014/10/01/why-bitcoin-is-and-isnt-ideal-money/

Danny Hamilton, you're not smart enough or important enough to back up how much of an asshole you are.  Maybe take it down a few notches, especially when you're wrong and making a fool of yourself.

And yet the quote that you've posted specifically states:

Satoshi had already more or less decided on a 50-coin per block payout with halving every so often

So it appears that the 21 million is the derived amount that "50-coin per block payout with halving every so often" would "add up to".

That post you quoted isn't about how the 21 million was "decided", it is about the divisibility.  It starts by pointing out that the "50-coin per block payout with halving every so often", which results in 21 million, had already been decided (but says nothing about why it was chosen), and then goes on to explain why 10⁸ subdivisions were chosen.

I'll try not to be such an asshole in the future, but for some reason my patience always seems to run out when I'm dealing with you.

[runpaint]

So instead of 21 million, he ended up deciding to multiply that number of units by 100 million.  That's kind of different.

And if you follow the links, there is even more commentary on the limit of 21 million bitcoins -

A 32bit signed integer can represent numbers from −2,147,483,648 to 2,147,483,647

if you wanted to do accounting for modern currencies with pure integers due to denomination factor of 100 (1$ = 100 cents)
then the obvious choice is to work in cents
Code:

       1 -> 1 cent
     100 -> 1 $

in such a system the most you can represent is slight above 21 million $
Code:

   from  −21,474,836.48 $      to       21,474,836.47 $

Note that left of side of the dot there are 8 digit/decimal places (21 xxx xxx).
Lets assume 1BTC worth(represents) 1 $.
To make it symmetric the dynamic logarithmic range has to be [ 10E-8 , 10E8 ]
This range permits exponential growth or decay for 2*8 orders of magnitude!

As for this:

I'll try not to be such an asshole in the future, but for some reason my patience always seems to run out when I'm dealing with you.

Yeah it's just me, and also the entire ignore list you're sharing so that everyone else can also ignore the people you ignore.

[neurotypical]

So that if all gold speculation goes to Bitcoin (at the prices of 2009) the price of bitcoin would be 1000000$

If bitcoin goes above all electronic payment methods it would be around 240.000 USD per coin.

[jonald_fyookball]

yeah basically derived as other have people have mentioned. 50x210,000 will give you half that, and then you double it for the infinite series.  the 210,000 is just a round number representing 4 years of 10 minute blocks.

[josef2000]

The question is-why not?

[ebliever]

Oh, I thought it was obvious. 21 million. 21 is half of 42, the answer to Life, the Universe and Everything. But Bitcoin is only only half the answer, because money isn't everything. And 21 million instead of 21 because 21 would make it sound like a blackjack game. There, does that make sense? (OK, I'm in a weird mood right now... ;-)

[lolled]

Pretty sure, it was not a random number picked up. It was derived from a lot of thing, and he also thought about the future of the coin while doing that

[RedhatCAT]

My understanding is that the initial 50 BTC block reward was an arbitrary number, as was the 210k number of blocks between the times that the block subsidy chances.

The 21 million number is simply the result of using the two above arbitrary numbers. (although the fact the initial block reward and the number of blocks between block subsidy changes being arbitrary is speculation, I do not see any other reasonable explanation)

[teukon]

In a slightly earlier version of Satoshi's code (pre-genesis) the limit was 20 million bitcoins.  Blocks were set to arrive every 15 minutes with an initial subsidy of 100 BTC set to halve every 100`000 blocks (about 2 years and 10 months).

Certainly there was some thought put into the magnitude of the limit.  While Satoshi had 63-bits of space to play with (using signed 64-bit integers at the time) it seems possible that he intentionally confined bitcoin amounts to well within 53-bits so that amounts could be handled comfortably by the IEEE 754 binary64 datatype (potentially useful for JSON-RPC).

What we can be reasonably sure of is that the particular figure of 21 million arose simply as part of some last-minute tweaking and carries no deeper meaning.

[runpaint]

In a slightly earlier version of Satoshi's code (pre-genesis) the limit was 20 million bitcoins.  Blocks were set to arrive every 15 minutes with an initial subsidy of 100 BTC set to halve every 100`000 blocks (about 2 years and 10 months).

Certainly there was some thought put into the magnitude of the limit.  While Satoshi had 63-bits of space to play with (using signed 64-bit integers at the time) it seems possible that he intentionally confined bitcoin amounts to well within 53-bits so that amounts could be handled comfortably by the IEEE 754 binary64 datatype (potentially useful for JSON-RPC).

What we can be reasonably sure of is that the particular figure of 21 million arose simply as part of some last-minute tweaking and carries no deeper meaning.

Sounds reasonable to me

[MegaHustlr]

As  escrow.ms shared , the link provides a proper mathematical explanation on this

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.

[A.F.K]

21 million was not chosen, 21 million is the result of multiple other choices.

Initial block reward was 50BTC
1 block is made every 10 minutes
Block reward halves every 4 years

Those three choices lead to 21 million coins, after so many halvings the block reward eventually hits 0 and at that time the number of coins generated happens to be just under 21 million.

Nice answer, thanks for spelling it out like that.

[redsn0w]

I think it is correlated with "gold" , but I'm not sure (surely I'm wrong).

[pedrog]

As a play on the ridiculousness of the legal age to drink alcohol being 21

Legal drinking age is 18 in many European countries.

16 in my country, but soon to be 18.

Total number of bitcoins to ever exist is 20999999.97690000, a little less than 21 million.