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Per https://etherscan.io/address/0x0000000000000000000000000000000000000000 the zero account currently contains ETH worth about $3.3 million USD.

I understand how the zero account is used in the EVM. My question is who owns that Ether?

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Anybody who knows the private key for it owns it, but it's doubtful that anyone has that private key and it's unlikely anyone could brute force it before keccak256 is retired.

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