What miners are doing with those huge computers and dozens of cooling fans is guessing at the target hash. Miners make these guesses by randomly generating as many "nonces" as possible, as fast as possible. A nonce is short for "number only used once," and the nonce is the key to generating these 64-bit hexadecimal numbers I keep talking about. In Bitcoin mining, a nonce is 32 bits in size--much smaller than the hash, which is 256 bits. The first miner whose nonce generates a hash that is less than or equal to the target hash is awarded credit for completing that block, and is awarded the spoils of 12.5 BTC.
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