I have a handgonne that was hand turned on a lathe. (Blackpowder cannon on a stick, essentially. In this case, it shoots .357 bullets.)
Serial number is PS002. Meaning Phobos, Steel, number 002.
Lowest serial number the maker ever sold, in that he keeps the number 001's for his own collection.
For serial number-less guns, I have a couple Mossberg shotguns without serial numbers.
I would always confuse the clerks at my usual gunshop when I was stationed in San Antonio and could afford to buy more guns. Once I'd determined which specific guns of a model I was buying were identical, I'd start checking serial numbers for being prime using mental arithmetic. They could never understand why I thought it would be significant to find a prime numbered gun. (I never did.)
At some point over the next couple decades, I hope to purchase and finish some of those 80% 1911 frames. Get a stamp set, and give them serial numbers that are actually messages to my next of kin. I think it would be a beautiful thing to leave an inheritance of a gun with the serial number "Don'tEverGiveUp,Johnny" or somesuch.