This question already has an answer here:
Should a passport number or visa number be in the class of personally identifying information, along with things like a social security number, credit card number, and so on? If someone nefarious did get my passport number or visa number, what could they do with it, without having the actual passport?
I know you can use an SSN and a bit of social engineering to get pretty much any other identity document, and a credit card number can potentially get you into a lot of online accounts at the very least, but passport numbers aren't so widely linked to other information and I'm curious about what could be done with them.
Of course I'm not actually about to go sharing my passport number around in public - better safe than sorry, after all.