4177725 was produced 21-Jul-1993
Engine Serial Number: 4177725
Engine Type: ROTAX 618 UL
Model Number: 306180010
5432355 was produced 21-Mar-2001
Engine Serial Number: 5432355
Engine Type: ROTAX 503 UL FAN
Model Number: 305030010
As for the others, they all predate the electronic database system.
3975034 : "Your Engine is not listed in the system"
3443750 : "Your Engine is not listed in the system"
3476289 : "Your Engine is not listed in the system"
4937458 : "Your Engine is not listed in the system"
We were able to examine the North American distributor's paper archives, and none of those engines are listed there either. Possibly they originated with a European distributor. It's also possible that some of them could actually be snowmobile engines. But based on the paper records, the numbers indicate they are likely from the following date ranges:
377 = 3443750 : Mid-80s, probably 1985
377 = 3476289 : Mid-80s, probably 1985
503 = 3975034 : Late 1990-early 1991
503 = 4937458 : 1999 (spring)