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I don't see how it is not the case that mining Bitcoins is throwing away energy.

The 'work' is actually the verification of transactions on the blockchain - the reward from mining is just an incentive to do this (mining & verification are tied up in the same process).

The energy expended in mining is necessary to validate transactions in the network.

You might be able to make it more energy efficient but you can't remove the energy expenditure.




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