You just found the application you were looking for to find out your SIM Serial Number (also known as ICCID).

With this simple application you're going to be able to read your SIM Serial Number without the need to take out of the device the SIM itself.
This serial number is used for many reasons, among them transfering to another mobile network operator.

The app supports double SIMs devices as well and displays your Serial Number (ICCID), carrier name as well as phone number.