You answered Jason's questions so very well, I wonder if you could help me. I, too, inhereted a Remington 760 Gamemaster 30.06. I believe the ID number is 275966, and the three letters on the left side of the barrel are R.E.R. (I am not sure the last letter is an R. It was worn.)
Do you need anything else? My brother-in-law was also from Pennsylvania and love to hunt deer, but he passed away some years ago and his wife gave the gun to me.
Jake, I believe the letters that you mention stand for Remington English Proof (REP). The date code would be on the other side and would be two letters. The second letter (year) would be a "B or C" indicating 1955 or 1956. So check for them. I have a 760 # 287xxx which is a bit later than yours and the code on it is "DC" August 1956. Keep us posted, ken
For the last 50 years I have used a Rem. 760.... . 35 Rem, if ever a better gun was made someone kept it for themselves! Don't worry about serial numbers, just enjoy the quality of the product. Life is too short to worry about all that techinical baloney.
Regards, and shoot straight.