Hmm, I somewhat disagree. Private information is anything you don't want public. By protocol, it isn't strictly private. But a phone number is private/unknown until its known, which is how most of us prefer it.
For example, in implicit social code it is impolite to give away a friend's phone number without asking them first.
The gray area for that is sharing a business phone number of your friend that they share widely through business cards or their website. Though typically it ends up being an email introduction if you really care to connect someone with your friend.
For example, in implicit social code it is impolite to give away a friend's phone number without asking them first.