3346610 is not in the factory's electronic record system.
We do have paper records going back earlier, but I could not find it in there either.
If 3346610 is the correct number, (not a typo?) then probably it was manufactured before 1985, as we have records of some 335xxxx engines sold in 1985 - and that's about as far back as we go on paper.(We only have North American paper records here)
Are you certain it's a 503 aircraft engine? (Our two stroke records expert thinks that the 334xxxx range might be assigned to snowmobile engines.)