# Is the number of coins limited by rule or by computational infeasibility?

it is well known that the upper limit of bitcoins is 21 million, which can be calculated mathematically; but from documents i have read, this is because mining a new block is defined to have diminishing returns (1 halving per 210k blocks); is this the sole factor limiting the possible number of coins? is there anything i missed in this crypto system which becomes more and more difficult over time and finally becomes computationally infeasible that is limiting the number of coins?

## 1 Answer

No it does not become computationally infeasible, 1 halving per 210.000 blocks leads to a total of 21m due to math.

Bitcoin block reward is 50 for 210.000 blocks then 25 for 210.000 blocks then 12.5 etc. So the total reward is 210.000 * (50 + 25 + 12.5 + ...). Inside the parenthesis is a geometric series which can be rewritten as 50 * (1 + 1/2 + 1/4 + ...).

Now using the formula in the link we have `a = 50` and `r = 1/2` and the sum of this infinate series is 100. Multiply that by 210.000 and you get 21 million bitcoins total (actually a little less than that because a bitcoin is not infinately dividable).