i phone 13 pro max serial number

The letter “F” at the beginning of the serial number is irrelevant for the new/refurbished status. However, if the model number starts with F, it has been refurbished by Apple. What is the model number at Settings - General - About - Model = ???

M = New.

N = Replacement unit.

F = Refurbished by Apple

P = Personalized.

Macs and iPhones are sometimes returned almost immediately for "I wanted more storage" or "wrong color" issues. The device is verified as "fully functional" and has no "activation lock" issues, so should be just fine for you.

My 2011 MBP was off the refurbished list and still runs today.

I do not know how serial numbers work, but if the device functions and was sold by physical Apple Store I would not worry, especially if they sold AppleCare+ on it.

You are welcome.