Not really a serial number per se...
These would be the only numbers for your phone:
International Mobile Equipment Identity (IMEI) number, (serial number for LTE, GSM)
Mobile Equipment Identifier (MEID), (carrier serial number for CDMA)
Cellular Data Number (CDN), (usually for tablets?) maybe your cell number?
Integrated Circuit Card ID (ICCID) (SIM card id)
I could be wrong but thats what ive understood....