Satoshi has never really justified or explained many of these constants.
it is someone found out about this constants yet?
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1Are you looking for the description of the formula?– MCCCSCommented Apr 2, 2018 at 12:43
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2 Answers
It is still unclear how Satoshi chose all the constants present in the Bitcoin protocol (10 mins blocks, 21 million coins, 2016 blocks intervals, etc...).
While we'll never know for sure the full justification until Satoshi manifests itself, we can try to come up with reasonable ones ourselves.
For example, it is supposed the total number of satoshis in existence has been chosen to fit in 64 bits (using a number larger than 64 bits would have made the implementation more complex), making the difficulty interval a power of 2 simplified a lot of maths, etc..
The formula above shows the total supply to be created. The block rewards will halve 32 times before 2140. While the reward halves, Bitcoin has 8 digits (in the mantissa) after the decimal point, so there's the floor function to truncate. The reward becomes half when "i" is incremented, and there are 210000 blocks between the halving. Since we multiplied the reward by 10^8 to find satoshi value, we're dividing it by 10^8 at the end.
