Re: 2nd factor strong!
"Cynical translation: Google wants your phone number"
Not that I necessarily disagree, but assuming you happen to have an Android phone that you actually use as a smartphone (ie. associated with your Google account) they probably already know your phone number even if they pretend to not know it for your ease of mind. To be honest, I'm willing to jump through some pretty outlandish hoops to preserve _some_ semblance of privacy - but not checking my mail on my smartphone is NOT one of them.