If it has the original barrel serial numbered to the action, then a rollstamp on the barrel of "E Remington and Sons" will be antique. Some "Remington Arms Co." are antique, but not all. 
If it has a steel forearm cap it is also antique, as the plain wood with ebony V came late in production.
It's estimated that approximately 1200 guns were made each year from 1880 up to 1885, and they started with #1 and went forward from there. So about serial #6600 was the cutoff for the early rollstamped guns. Reorganization took a couple years or more before guns appeared with the later marking, and that puts them in  the late 1880's. At that point they resumed but continued to use earlier marked barrels, so they are found up to around serial #7200. Total production numbers go up to around 10050, but there are many missing numbers totaling around 100 in the changeover to the new owners, so less than 10,000 total made. 
So based on the later production of approximately 3,000 guns over 15 years to end of production in 1904, it would likely have to a higher number than #9,000@ to be modern. At around serial number I 9890 they added that "I" prefix, so all I prefixes are for sure modern. 
Clear as mud huh? Wish I could tell you an exact number, but most consider that #9000 as a general cutoff, but it might be higher. The I prefix is a really firm cutoff for modern.

You're welcome Tom. Hope it helped at least a little in determining age.

Cw, that brings up a good point on Hepburns, and many old single shots. We need to ensure they're all matching numbers before we use a particular example to determine what is correct or original.
In the back of Rowe's book on Hepburns are a good number of examples of Hepburns by serial number, but many were not original guns, so the data is skewed. I know of several listed there that info was sent to him, but no notation in the book stating they'd been reworked, rebarreled, or altered. So now it's in print, and those reading that info will assume it's been documented and double checked.

I'd think your guess is pretty close. 1882-1883 I'd guesstimate. Have to double check one of mine to be sure, but I believe Remington serial numbered stocks. So you might remove the forearm and check both the barrel channel, and the rear surface. Same for buttstock. Remove and check tang area, and under buttplate.

My Hepburn is a U.T. Browning Bro's marked gun with ebony fore arm tip. Utah statehood was 1896, so apparently the mfg. date was prior to that. How long did the Browning's mark territorial guns from their shop?
regards
kw

well when I was cleaning up the wood ,I found 2678  stamped on both the upper and lower tang left side but the s/n on the receiver and barrel  25xx ?

boommer wrote on Nov 12^th, 2018 at 12:32am:


The numbers on the tang sides are not serial numbers. They are assembly or work order numbers. My Match B is #85xx, but the tangs are #157.
You should also look closer at the wood, as the ends of the forearm and buttstock should have serial numbers matching the gun's serial number. On the forearm it will be on the raised rectange of wood that goes into the receiver. On the buttstock it will be on one of the two raised rectangles of wood that slip into the action. Usually on the right side one.