I'm not registered with Facebook and I've never logged in to Facebook inside the browser I use, Today I enter the site facebook.com and see my actual phone number on the sign in page with this message:
Facebook requests and receives your phone number from your mobile network
So how does a website, in this case Facebook get the mobile phone number inside the browser?
Basically your mobile phone company is adding your phone number to HTTP headers when you visit certain sites.
So when you visit www.advertiser.com your request goes to your mobile phone operator, via cell towers, through their network, off to the internet
Obviously the cell tower knows your number, as does your phone operator, they configure their router to add some more headers to your HTTP request (unencrypted) because the owner of advertiser.com pays them to do so.
This extra data is then sent over the internet to www.advertiser.com who can simply parse it out of the headers and put it back in the <input> tag in the response.
facebook are being quite open about this here. But they will also get the phone number, along with the website url of every site you visit with a like button somewhere on it. Which they then store on a big database in china
http://www1.icsi.berkeley.edu/~narseo/papers/hotm42-vallinarodriguez.pdf
Given fields are remembered by browser, so for example if I enter some store (online), and they use the same field keys as other stores a lot of input will be filled automatically (by browser).
If it is the source of your phone number, I would check the browser settings to exclude remembering digits. If not, it might happen you enter some pin-code or something, on another site there will be the same field key, but hidden so you even don't know when the browser will do auto-completion for you and send sensitive data.
Facebook requests and receives your phone number from your mobile network.
Without confirming, that sounds literal to me. This is, it sounds like Facebook literally just asks your mobile network provider to tell them your number.
I'd imagine it works like this:
Some Facebook page wants your mobile number.
Facebook checks what provider's IP address range your IP address is in to determine your provider.
Facebook sends a request to your provider to the effect of:
Hey, we got traffic from a user at
123.123.123.123, which is an IP address within your service's range. What's their number?
Then, I guess, your mobile internet provider may choose to respond to Facebook's request.
It's probably an automated service that they've got set up. Such a service would seem pretty easy to implement and run on a technical level; the major hurdles would seem to be legal/political.
From Facebook:
We may suggest a mobile number for you based on information we receive from sources such as:
Your mobile phone or tablet.
Contact info provided by others on Facebook.
A mobile number that you entered previously but didn't confirm.
So as Facebook describes it, they may try to pull phone numbers from multiple sources.
