Bitcoin's Total Supply Equation

Model: GPT-4



In the context of Bitcoin please explain the equation 32 Sigma 2,100,000 next to in parentheses 50/2i

The equation you mentioned is related to the Bitcoin mining process, specifically the block reward halving event that occurs approximately every 210,000 blocks. The equation is used to calculate the total supply of Bitcoin that will ever exist, which is capped at 21 million. Here's a breakdown of the equation: 32 Σ (2,100,000 * (50 / 2ⁱ⁾⁾ This equation represents the sum (Σ) of a series of terms, where "i" varies from 0 to 32 (inclusive). Each term in the series calculates the number of Bitcoins mined during a specific reward era (between halvings). Let's break down the components of the equation:

32: The number of iterations (from 0 to 32) that covers all the halving events in Bitcoin's history until the mining reward becomes negligible.

Σ: The summation symbol, which indicates that we are summing up the values of the series for each value of "i".

2,100,000: The number of Bitcoin mined during each era. This number is derived from the fact that there are 210,000 blocks in each era and the initial block reward is 50 Bitcoins. So, 210,000 * 50 = 2,100,000.

50 / 2^i: This part of the equation calculates the block reward for each era. The initial block reward is 50 Bitcoins, and it halves every 210,000 blocks (roughly every 4 years). So, for each era, the block reward is 50 divided by 2 raised to the power of "i" (where "i" is the era number).

When you sum up the series with "i" ranging from 0 to 32, you'll get the total number of Bitcoins that will ever be mined, which is approximately 21 million. Please note that the equation you provided isn't a standard notation or commonly referred to in the Bitcoin community, but it helps explain the concept of block reward halving and the 21 million Bitcoin supply cap.