The Beginner's Guide for Smogon doesn't list the /alts command for some reason, so I asked TGA, who is Voice is the Help room.
Here's what he said:
Hence, the /alts command shows your main account, Rooms, IP address and recent battles within the past 15 minutes.
(My main account is asjklfjsdklfjsdfjl.)
The "private number" you're talking about is your IP address. But don't worry, no one other than you can see the information given by the alts command, or the alts message itself. That goes for all commands starting with "/" -- they're meant only for you to see.
When I used the /alts command for the first time even I thought I leaked my IP to hundreds of people, so I asked a staff member to clear my message but they said only I can see the /alts message.
Source: Experience
Hope this helps!