Playing around generation of vanity addresses, I've discovered that private keys are stored as base58 numbers, with the character "5" at the beginning.
The reason why public keys are distributed in base58, I can understand: base58 is a kind of base64 without some conflicting characters that could be confused and taken as phising target.
But, private keys never should be cast out. So, base64 seems to be perfect for the goal, because it is the easiest way to "textify" binaries, the most compact and most universal.
For example, the private key:
In base64 (excluding the starting "5"):
Any clues for this strange election?