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How can the generation of a vanity address be accelerated?. How can the brute-force algorithm be improved beyond trying a bunch of randomly selected private keys?

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How can the generation of a vanity address be accelerated?.

By applying better hardware, faster CPU and GPU hardware. Or more of them.

How can the brute-force algorithm be improved beyond trying a bunch of randomly selected private keys?

If anyone knew an algorithm better than brute-force search for discovering the private key for a partial address, I believe Bitcoin would probably be broken and unusable.

RedGrittyBrick
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