A hash cannot be predicted in advance
A miner changes the nonce and other block-header fields, then calculates a hash. The result looks random: there is no shortcut for finding the correct value without a very large number of attempts.
The network sets a target threshold. The lower the target, the fewer hashes qualify and the higher the difficulty. When the network's total hashrate changes, the protocol adjusts difficulty so blocks continue to arrive at roughly the intended interval.
- a miner cannot choose the winning hash in advance
- each new attempt has a very small probability of success
- checking a completed solution is far cheaper than finding it
Why this protects the network
Every block points to the previous block's hash. If an old transaction is changed, the attacker must recalculate that block and every block after it while honest miners continue working in parallel.
That is why Proof of Work is not pointless number crunching. It is a mechanism that makes an attack expensive in both computing time and electricity.
Real photos and source material
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