I never had a prop log until it was overhauled. Does a fixed pitch prop even come from the factory with a log book?
Most definitely -- with serial number. (How did your plane get annualed without a prop log book?)
My old prop had a logbook that went back to 1968. The prop had been overhauled 10 years ago, and inspected yearly.
I mentioned in an earlier post that there's a guy trying to sell a new in the box, 16-year-old McCauley 1A101/DCM 6948, but no log book (apparently it was lost). My mechanic tells me that, no matter how new and nice it is, we'd still need to send it to a shop to have it checked, and get a logbook started.