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They don't verify transactions actually. That is what nodes do. They retrieve valid transactions from nodes, order them, and then hash them according to the consensus proof-of-work algorithm, which in this case, is SHA-256, until it produces a block that will satisfy the node consensus requirements.

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Miners are nodes and therefore verifying transactions, and they're the only nodes writing transactions to the blockchain.

Non-mining nodes can only verify transactions for themselves , which helps them stay on the chain of their choice but does not extend any chain.

Miners require nodes, so they have them too, because without nodes they can't source transactions. Every node, applying consensus rules, extends the blockchain by accepting valid blocks that meet consensus rules.

We have had a year long education in the limited power of miners with many people incorrectly attributing responsibility for maintaining the protocol. Miners were rightly shown to be powerless to force consensus changes on the nodes. When push came to shove they did what they were told, at the threat of being crushed with a pow change.

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