This is one of the most poorly understood elements of blockchain technology, yet it is absolutely crucial for the accuracy and immutability of the Bitcoin blockchain.
The fundamental idea: a miner earns the privilege of creating the next block by proving it has done the computational work required. The reward is both the block reward (newly created BTC) and transaction fees.
The process: each miner collects transactions from the mempool, adds the hash of the previous block header, and creates a new hash of all this combined information. The miner then checks whether this hash meets the current requirement — that the binary representation starts with a specific number of zeros. If not, the miner adds a nonce (a number) to the data and rehashes, repeating until a valid hash is found.
As computing power increases, the difficulty level is adjusted — more leading zeros are required — to ensure new blocks are added approximately every ten minutes.
This is what articles mean when they refer to "complicated equations miners have to solve." It is simply adding nonces to data until the hash satisfies the difficulty requirement.
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