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.
Topic: Why exactly 21000000 BTC (Read 353 times)
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
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
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.
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".
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".
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
You can see accurate figures here: https://en.bitcoin.it/wiki/Controlled_supply#Projected_Bitcoins_Long_Term
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
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
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.
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.
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
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
OP, good question! Hahaha. 
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.
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.
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?
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?
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.
Quote
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.
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.
Quote
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.
* 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.
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/
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 <[email protected]>
Date: Sun, Apr 12, 2009 at 10:44 PM
To: Mike Hearn <[email protected]>
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!
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
Quote
From: Satoshi Nakamoto <[email protected]>
Date: Sun, Apr 12, 2009 at 10:44 PM
To: Mike Hearn <[email protected]>
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!
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.
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
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.
Quote
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...
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.
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.
Quote
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.
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 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...
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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