Why exactly 21000000 BTC

[Isabela Kaif]

Why did Satoshi make the supply exactly 21 million. They would select 20 million or 50 million or any amount. Is there any particular reason why the amount is 21 million?

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[jackg]

I think the whitepaper suggests that if 1 Satoshi was 1 cent then there'd be enough to cover the currency market in general and allow for a stable liquidity of assets.... I think he must've just like the number though personally...

[UserU]

Well, nobody truly knows but according to this article from TNW, there's some mathematical equations involved regarding the halvening. Just take this with a pinch of salt.

Nakamoto explained why they chose 21 million for Bitcoin‘s supply limit, but never really expressed how.

One solid theory involves dissecting Bitcoin‘s distribution model (which had been hinted at in the Hearn email), but it unfortunately requires some mathematics.

Many believe that Bitcoin‘s 21 million limit was arbitrarily set when Nakamoto made two key decisions, that: Bitcoin should add new blocks its blockchain every 10 minutes (on average); and the reward paid to miners (starting with 50 BTC) halves every four years.

A post on the Bitcoin section of popular dev forum StackExchange suggested Bitcoin‘s 21 million supply limit is more of a mathematical coincidence than a conscious choice.

Calculate the number of blocks per four 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.

[o_e_l_e_o]

You can read the first mention of the 21 million coin limit in Satoshi's "Bitcoin v0.1 released" email here: https://satoshi.nakamotoinstitute.org/emails/cryptography/threads/2/#014994

Total circulation will be 21,000,000 coins. It'll be distributed
to network nodes when they make blocks, with the amount cut in half
every 4 years.

first 4 years: 10,500,000 coins
next 4 years: 5,250,000 coins
next 4 years: 2,625,000 coins
next 4 years: 1,312,500 coins
etc...

Given that the bitcoin white paper already talks about aiming for a 10 minute block time, and the genesis block was mined a few days before this email with a reward of 50 BTC, then I think it is reasonable to assume that the 21 million limit was picked based on the timeline and accumulation of block reward halvings, rather than the 21 million limit being picked first and the block reward and halving times being calculated to fit it.

[jackg]

Probably security reasons and for an ease of understanding. In saying what you've said we could have a dynamic reward every block to reduce the earnings by a certain amount but I think an event every four years where the new block reward was determined makes it easier to calculate how much you'd get from a block and how well you could profit. It also makes the calculations a lot easier later on. I'm not sure what the last block reward will be but there may be div2 underflow errors involved in producing a reward on your schema.

[aoluain]

According to Satoshi the total amount was "an educated guess"
and yes it is related to current currencies and how Bitcoin can
be decimalised, here is an extract from a mail sent back in 2009

From: Satoshi Nakamoto <satoshin@gmx.com>
Date: Sun, Apr 12, 2009 at 10:44 PM
To: Mike Hearn <mike@plan99.net>

My choice for the number of coins and distribution schedule was an educated guess.  It was a difficult choice, because once the network is going it's locked in and we're stuck with it.  I wanted to pick something that would make prices similar to existing currencies, but without knowing the future, that's very hard.  I ended up picking something in the middle.  If Bitcoin remains a small niche, it'll be worth less per unit than existing currencies.  If you imagine it being used for some fraction of world commerce, then there's only going to be 21 million coins for the whole world, so it would be worth much more per unit.  Values are 64-bit integers with 8 decimal places, so 1 coin is represented internally as 100000000.  There's plenty of granularity if typical prices become small.  For example, if 0.001 is worth 1 Euro, then it might be easier to change where the decimal point is displayed, so if you had 1 Bitcoin it's now displayed as 1000, and 0.001 is displayed as 1.

https://pastebin.com/Na5FwkQ4

As an aside we can see here that Satoshi realised the initial interest
in Bitcoin would be small but he was also thinking ahead  and how
Bitcoin could be become fractions in a wider application with greater
popularity.

When Bitcoin reaches €10,000 again €1 will be worth 0.0001BTC,
similar numbers to what Satoshi wrote above but on a far greater scale!

[boyptc]

it could be arbitrary number.

I have read an article about this and it says exactly the same thought.

--> https://beincrypto.com/why-did-satoshi-nakamoto-choose-21m-as-bitcoins-maximum-supply/

[seoincorporation]

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.

That explains it...

21 million sound as a small number for some people, but it has a trick, if you focus in the number of zeros after the dot then you will realize how big is the number and how 21M of bitcoin really could be: 2,100,000,000,000,000 units called satoshis.

So, 21M is a tricky number.

[FaithInCrypto]

Well, nobody truly knows but according to this article from TNW, there's some mathematical equations involved regarding the halvening. Just take this with a pinch of salt.

Nakamoto explained why they chose 21 million for Bitcoin‘s supply limit, but never really expressed how.

One solid theory involves dissecting Bitcoin‘s distribution model (which had been hinted at in the Hearn email), but it unfortunately requires some mathematics.

Many believe that Bitcoin‘s 21 million limit was arbitrarily set when Nakamoto made two key decisions, that: Bitcoin should add new blocks its blockchain every 10 minutes (on average); and the reward paid to miners (starting with 50 BTC) halves every four years.

A post on the Bitcoin section of popular dev forum StackExchange suggested Bitcoin‘s 21 million supply limit is more of a mathematical coincidence than a conscious choice.

Calculate the number of blocks per four 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.

I've been asking myself the same question recently as to where did that 21M originate so I guess this explains why. This is something a mind like I have would not understand if I don't read the comments carefully.

[Kemarit]

Going back as early as 2011, this sort of question has been asked,

Why IS the bitcoin limited to 21 million?

Why 21 million bitcoins? Why was ~that~ number chosen?

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

[Wind_FURY]

OP, good question! Hahaha.

I think the whitepaper suggests that if 1 Satoshi was 1 cent then there'd be enough to cover the currency market in general and allow for a stable liquidity of assets.... I think he must've just like the number though personally...
 

Would the number "21" be one of the clues on Satoshi Nakamoto's real identity? Was he 21 years old when he started working on Bitcoin? Or is his birthday on February 1?

I believe behind everything, is a man who wants to be found.

[frank0ly]

A few links about this

https://bitcoin.stackexchange.com/questions/8439/why-was-21-million-picked-as-the-number-of-bitcoins-to-be-created

https://thenextweb.com/hardfork/2019/07/08/heres-why-satoshi-nakamoto-set-bitcoin-supply-limit-to-21-million/

https://www.quora.com/Why-do-we-only-have-21-million-Bitcoins

[wozzek23]

Why did Satoshi make the supply exactly 21 million. They would select 20 million or 50 million or any amount. Is there any particular reason why the amount is 21 million?

We can only know this one if Craig Wright is the real Satoshi.
Honestly, there are so many beliefs about this one and you can read it on google, some article says its a personal reason of Satoshi, some also say that it comes from a bigger solutions and formula but none of them is accurate and sure.

For sure, Craig wright might not be the real satoshi, but it is not the main question here. Satoshi was a brilliant individual who so ever he is so I would prefer not doubting his creation. Might be there is some logic behind why he choose 21M bitcoins only into existence. There are thousands of minds liberating thousands of views and not each of them might be reliable.

There are a lot of people who already are been predicting the main reason behind why only 21M bitcoins but there is none(except the real satoshi) who knows the real reason behind it. It perhaps is a mystery which would hardly be solved even after those 21M bitcoins are all out for usage.

[Tash]

It will never reach 21 Million. If you use 8 decimal places 1 satoshi reward is reached after 33 halvings

Code:

        Reward           New Coins produced in 4 years
2009	50,00000000		10500000,00000000	
2012	25,00000000		5250000,00000000	
2016	12,50000000		2625000,00000000	
2020    6,25000000		1312500,00000000	
2024	3,12500000		656250,00000000		
2028	1,56250000		328125,00000000		
2032	0,78125000		164062,50000000		
2036	0,39062500		82031,25000000		
2040	0,19531250		41015,62500000		
2044	0,09765625		20507,81250000		
2048	0,04882813		10253,90625000		
2052	0,02441406		5126,95312500		
2056	0,01220703		2563,47656250		
2060	0,00610352		1281,73828125		
2064	0,00305176		640,86914063		
2068	0,00152588		320,43457031		
2072	0,00076294		160,21728516		
2076	0,00038147		80,10864258		
2080	0,00019073		40,05432129		
2084	0,00009537		20,02716064		
2088	0,00004768		10,01358032		
2092	0,00002384		5,00679016		
2096	0,00001192		2,50339508		
2100	0,00000596		1,25169754		
2104	0,00000298		0,62584877		
2108	0,00000149		0,31292439		
2112	0,00000075		0,15646219		
2116	0,00000037		0,07823110		
2120	0,00000019		0,03911555		
2124	0,00000009		0,01955777		
2128	0,00000005		0,00977889		
2132	0,00000002		0,00488944		
2136	0,00000001		0,00244472		
2140	0,00000001		0,00122236		
Total	99,99999999		20,999,999.99877764	

[o_e_l_e_o]

Some of your calculations are a little off. When an odd number of satoshis is halved, the result is rounded down, not up. The actual upper limit of bitcoin is 20,999,999.9769, provided the subdivision in to 8 decimal points isn't changed at any point. If we changed to millisatoshis like on the Lightning Network, the final upper limit would be slightly closer to 21 million.

You can see accurate figures here: https://en.bitcoin.it/wiki/Controlled_supply#Projected_Bitcoins_Long_Term

[Wexnident]

Probably a good estimation regarding the supply in terms of time frame from Bitcoin's release to the last coin mined? The last BTC would be mined at around the year 2140, and BTC starting in 2009. Counting the years, there are about 131 years in that time frame. The rest would be fitted into that time frame such as the BTC mining limit and the halvings every four years.

As for why it is 131 years, and not above or below, Satoshi could've thought that a century is enough for BTC to completely assimilate itself towards the world, and become a part of its trading as the global currency. Well, I also found some meaning behind the number 131 which may be absolute bs, but let me share nonetheless. 131 means clearing away negativity and discouragement and cultivates a positive awareness to transform your life. For those curious, just look up " the number 131".

[davinchi]

Why did Satoshi make the supply exactly 21 million. They would select 20 million or 50 million or any amount. Is there any particular reason why the amount is 21 million?

There might be no specific reason behind why satoshi created 21 million bitcoins but as far as I can guess, I think 21 was a lucky number for satoshi which made him create 21 Million bitcoins only. Perhaps 21 might be birth date of his loved ones or something like this if we think farcically. There is not always a reason behind why something like this is been numbered.

Satoshi was/is a great personality with a great mind and hence he might have encountered with a number of 21 million for some or the other reasons. Perhaps he would have calculated the mining speed of bitcoins and would have predicted the exact time or day when those 21 million bitcoins would completely be mined out so that something more exciting some in between the blockchain network.

[Tash]

 Roman
 21=XXI


 Binary
 21=10101
1010000000110111101000000

Japanese


If it is correct or not i will never know 20,999,999.97690000
https://www.wolframalpha.com/input/?i=%28sum%28210000*floor%285000000000%2F2%5Ei%29%29%2C+i%3D0+to+32%29


Sum of the first six natural numbers
(1 + 2 + 3 + 4 + 5 + 6 = 21)
     △      1
    △△     2
   △△△    3
  △△△△   4
 △△△△△  5
△△△△△△ 6

[HarmonyA]

21 million was an informed supposition .
As per an email shared by Hearn, Nakamoto proposed Bitcoin's unit costs to in the end line up with conventional fiat monetary forms.

In the event that Bitcoin stays a little specialty, it'll be worth less per unit than existing monetary forms. In the event that you envision it being utilized for some portion of world trade, at that point there's just going to be 21 million coins for the entire world, so it would be worth a lot more for every unit.