I have never seen a No 4 without a serial #. Look on the bottom of the barrel ahead of the forearm.
With a round barrel it should have a thumb screw take-down system. They were made from 1924 to 1933 so it should also have a date code that will tell you the month/year of assembly. The key for the code is on the home page of this site.
Let us know what you find out.
remington rolling block model 4 22
Re: remington rolling block model 4 22
Sounds right to me. Enjoy your No. 4...