I have a number that was on the back of the Singer machine head. 3151727, I wanted to know what model this is. I couldn't find the model # on the singer site.

If that is a serial number, then that is an older machine. The #'s aren't usually on the back of the machine head, however, so ???

All the (deleted) Singer files had to say was
serial #'s 2.925.000 to 3.679.999 - numbers allocated in 1879

They don't have model numbers for everything, but if you post a picture someone will probably be able to identify it for you.

Where on the back? My 9W has the serial on the back instead of in front of the post...in which case it would have been made between 1906 and 1912. :)

I saw that on the singer site, the lady that has the machine said it doesn't have any dots, it is a solid number. She is going to give the machine to me. I will know more after I get it. The number was on a little gold label on the back. This lady is in her 70's, she said it was her grandmothers, so it could be that old. I am excited to get it.