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Yes, 80 ^ 7 has the same order of magnitude as 3000 ^ 4. But passphrases are recommended because many folks can memorize a passphrase more easily than a password of equivalent complexity. Or because a typical user's idea of an okay password ("Johnny88") has less entropy than a passphrase.

Passphrases are unnecessary for users with a password manager, except maybe for the manager's master password.




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