Originally Posted by kamanwu
why my first login is pts/0, by my second login is pts/2?
does it mean that someone(unknown) login my server by using pts/1?
Nope, it doesn't mean someone else is login as pts/1. You may have got logged out Or disconnected from one of your session after you logged in the 3rd time to your server.
You can check the number of people logged in to your server using the 'w' command. It will show you the pts, they are connected to and the IP they are logged in from.