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I am setting up 2 node of private ethereum. Each node is miner. If in the future I have partner node. How can I how much ETH he mined from the network?

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Each mined block has a property that provides the miner's address. (see fourth line of this block informations)

As you obviously know your own addresses, you can loop through the blocks and check all the blocks which miner's address is not one of yours.

Knowing which blocks have been mined by your partner, you can extract as well the block reward (fifth line of the link bellow), add all of the together and as a consequence, know how many ethers has been mined by your partner.

To know which properties you need in detail, you may refer to this. If this is not up to date, you can spin up a node, use the geth API (for example) to get a block and check what's inside.

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