That particular plane is NB-52A, which was the last B-52A to be produced)
It is number 0003 and the name on its nose is "The High and Mighty One"
It launched the X-15 along with RB-52B, whose name was "Balls Eight" and number 0008. It was originally reconnaisance (hence the R)
You can go see either of these planes, the NB-52A is at Pima Air&Space museum; it is the oldest in existence. Balls Eight is at the entrance to Edwards.