First second and third Rome?
The 3rd is up in the air.
all laid claim on being the Third Rome.
Personally, I have to give it to the Ottoman Empire as the Third Rome; they event adapted the “Status Quo” notion from Rome and the Byzantine Empire and carried it through the centuries.
Russia I could see as a splinter of the Byzantine Empire perhaps; but it certainly went its own way and didn’t hold on to the ethos of Rome or Byzantium really.
I’d say the USA got the mantle for one of the Romes at some point – 4th or 5th if I had to put a number, but only domestically, not internationally.