Actually, the woman who rides the beast is Roman Catholicism. i.e. Babylon the Great. Scripture supports this with the following clues:
* The woman you saw is that great city that rules over the kings of the earth - Rev.17:18
At the time that John was receiving this information from the angel, the city that ruled over the kings of the earth was Rome.
* The seven heads are seven hills on which the woman sits.
So, the woman is a city and she sits on seven hills. Rome was literally built on and is famous for her seven hills.
* The woman was dressed in purple and scarlet, and was glittering with gold, precious stones and pearls.
Purple and scarlet are the exact colors worn by the bishops and cardinals:
Glittering with gold
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Roman Catholicism is figuratively called Mystery, Babylon the Great, because most of her rituals and practices originated from the religions of Babylon. You ever notice the Mitre hat that the pope wears closely represents the fish hat worn by the priests of Dagon the fish god? The split at top is the fishes mouth and there is even an eye. I would also mention the 82ft pagan obelisk from Hieropolis Eqypt that sits out in St. Peter's square.
The woman (Roman Catholicism) will ride the beast, meaning that she will use his authority and power to reestablish her religious authority, so that inhabitants of the earth will come under the authority of the pope and Roman Catholicism and that by force if necessary, just the way it was before 1798, except worse.
I believe that the false prophet will be none other than one of the future popes, who will be allowed to perform those miracles, signs and wonders on behalf of the first beast/antichrist and that for the purpose of giving credibility to his claim of being god.