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A bitcoin "brainwallet" is a secret passphrase you carry in your brain.
The Bitcoin Brainwallet Exponent Calculator is one of three functions needed to calculate the bitcoin PRIVATE key. Roughly, the formula is exponent = sha256 (passphrase)
Note that this is a bash function, which means you have to type its name to invoke it.
You can check the accuracy of the results here http://brainwallet.org
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