F I believe denotes of a serial number assigned to a refurbished unit. One that’s used by Genius Bar. They source the replacement phones from returns/defective handsets that are disassembled, fixed and returned to market via Genius Bar for warranty purposes. Genius Bar phones are not new—even if they do look like they are. (Actually some don’t, I’ve had issues in the past with a scratch here and there.)
Not true; mine starts with F and it’s a day one Verizon model iPhone X