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A bitcoin "brainwallet" is a secret passphrase you carry in your brain.
The Bitcoin Brainwallet Private Key Base58 Encoder is the third of three functions needed to calculate a bitcoin PRIVATE key from your "brainwallet" passphrase.
This base58 encoder uses the obase parameter of the amazing bc utility to convert from ASCII-hex to base58. Tech note: bc inserts line continuation backslashes, but the "read s" command automatically strips them out.
I hope that one day base58 will, like base64, be added to the amazing openssl utility.