Help Identifying Hierloom

It would be super helpful if you could pop off the back and show us what's inside. If you look closely around the edge, you'll probably see a small place to insert a sharp blade.

#2504 inside the case-back is the reference number. Here is the OVD entry:
https://www.omegawatches.com/en-us/watch-omega-other-omega-ck-2504

283 on the movement is the caliber.
http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&Omega_283

The 12M serial number suggests production in 1950-51 approximately.

I suspect that the sweep hand is not original to the watch.

Watchmakers often scratch or write a code in sharpie when they service a watch. Sometimes you can decode a date, but more often it is just an enigmatic series of characters. It's possible that the letters are initials, and the numbers refer to October 13, 2000. But you can't really be sure.

A given reference (e.g. 2504) would generally have been produced with quite a few different dial and hand-set variations, so it may not always be easy to find an exact match on the internet. As I mentioned, I think someone just installed that sweep hand as a replacement at some point. If you look at the OVD entry and search for other ref 2504, you will probably get a consensus idea of what the original sweep hand looked like. The "-10" after 2504 refers to the 10th production run of the reference. Sometimes watches made in the same production run share a common dial/hand-set, but not always.

You're very welcome.