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Bitcoin,I want to transfer some Amount so I broadcast a transaction that is picked up by miners. So if my transaction get's in 2 different currently processing blocks by different miners and one of them is mined into the blockchain, the second miner's block is dropped.

My transaction did, but also some transactions did not make it to the mined block.

How does the protocol know which transactions made it and which didn't? Another way of asking, how is a transaction "marked" as mined so if it's still floating in the p2p network, miners know that this transaction is already in the blockchain.

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How does the protocol know which transactions made it and which didn't?

Once a transaction is mined, all the network knows it's there. No one will keep it in their mem-pool any longer. Only before it's in the canonical chain you don't know who's seen it.

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the longest chain is always the chain which will be accepted by all nodes and miner. the other blocks in your scenario are called orphaned blocks. a good explanation for the longest chain is here.

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