That seems very high, honestly. You can usually find an R13 in the United States in the $1300-1500 range, unless it's brand new. Last time I sold an R13 it was back in 2017, but at that time one would be hard pressed to get much more than that for a used R13.
It's a little tough to tell from a surface glance if it's a real R13, but R13s will never have a model marking, and will always be made in France. Beyond that, it would take a closer look via pictures or in person to be able to tell for sure.