Your Primer embeds an RLink debugger/programmer. You connect to it in Ride and obtain its serial number the same way you would for an RLink.
Here is how to get the serial number of your Primer:
1. Launch Ride7
2. Choose RLink as Debug Environment in the ARM Advanced Options
3. Select Options > Project Properties > RLink Configuration > Advanced Options
4. Click on the box "Connect to RLink and Read Serial Number"