Yes, that's the serial number! I think Jon estimated my machine to be from 1889, and your machine's serial number would be above mine on the database list at the DVF yahoo group. The first serial number before mine (426889) on the list is 368663. That machine has a warranty date of 5/26/1887, your machine's number is only 22,290 numbers after that one, and I'd say your machine is most likely early 1888.
How cool!