For some reason, you might interest to know what is your iPhone unique number or a.k.a UDID instead of Serial number.
Here are Steps finding your UDID using iTunes
1. Open iTunes (the Mac or PC app, not iTunes on your iPhone).
2. Plug in your iPhone, iPod touch or iPad.
3. Click its name under the devices list.
4. Ensure you’re on the Summary tab.
5. Click on the text that says Serial Number. It should change to say Identifier (UDID).
6. Select Copy from the Edit menu.
7. Your UDID is now in the clipboard, so you can paste it into an email or message.