For those that contact Singer - be careful with what Singer sends you. They often don't ask what model you have, and if you "accidentally" send them the wrong number, you'll get the wrong information back.
I've had this argument with several people (most sellers on eBay) who said "Singer said" and what Singer said is obviously not correct. I think the vintage folk on this board know way more about the older Singers than what ever person they've got answering the mail/phone that may never have even seen what the machines they are looking up actually look like.
That is why it's always best to know what model you have, then if you look up the number and it shows it for a 15, and you know you have a 27, then it's time to take a closer look at the serial number. ISMACS site list dates and model numbers - and that list is a copy of what Singer is using.
There was one listing, the seller made up this cute little story about the Singer Red Eye made in 1915, and on and on. . . with the Singer certificate and all, unfortunately the machine was a 15-91 made around 1950. Which proves they'd never seen a Red Eye.
And then there is the one where they gave Singer the number of the motor, and were trying to sell it as a "pre 1900" machine. It was a model that was not made before 1900 - but they had a certificate from Singer to prove it!