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A public key is the public half of the public/private keypair. Anyone can use a public key check that a signature is correct, but they can't generate the signature themselves with the public key.

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How many different formats can a public address take?

I believe that the earlier format that you are referring to is the Hash160 which is formed by taking the sha256 of the public key followed by taking the ripemd160 of the result: Hash160 = ripemd160( …
Jon Lund Steffensen's user avatar