Bitcoin's code sets a hard limit on how many coins can ever exist. What is that limit?

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Answer

About 21 million bitcoins

The last fraction of a coin is not expected to be mined until around the year 2140, and millions of coins are thought to be lost forever in forgotten wallets.

How to estimate it

The limit follows from the mining rules. A block appears every 10 minutes, so 4 years contain about 6 × 24 × 365 × 4 = 210,000 blocks. The first 210,000 blocks paid 50 coins each: 10.5 million coins. The reward then halves every 210,000 blocks, and the series 1 + 1/2 + 1/4 and so on sums to 2. 10.5 million × 2 = 21 million. The cap is 21,000,000 bitcoins.

Source: Bitcoin protocol (Satoshi Nakamoto, 2008)

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