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How were the private keys for addresses like 0x0000000000000000000000000000000000000001 generated in ethereum? Surely they weren't made at random? Please let me know. How is it valid?

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There is no known private key for that address.

You don't need a private key to generate an address. You don't even need any fancy software. Just write 0x and add 40 hexadecimal digits of your choice:

0x012345678901234567890123456789ABCDEFABCD

There we go, we've just created an address without a private key. Don't send anything to such addresses, because those funds will be irretrievably lost.

https://etherscan.io/address/0x012345678901234567890123456789ABCDEFABCD

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