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What Is the Mathematical Function That a Miner’s Hash Rate Is Trying to Solve?

A miner's hash rate is the speed at which it can generate a hash output from a given input, which includes the block header data and a changing nonce value. The function is a cryptographic hash function, like SHA-256 for Bitcoin.

The goal is to find a hash output that is less than or equal to the network's current target difficulty. This is a brute-force guessing process.

What Is the Difference between SHA-256 and Keccak-256?
What Is the Difference between SHA-256 and a Simpler Hash Function like CRC Used in Other Data Integrity Checks?
How Is the “Target Hash” Calculated from the Difficulty Setting?
What Is the Difference between a “Share” and a “Valid Block Solution”?