Who is the False Prophet?

Then I saw another beast, coming out of the earth. He had two horns like a lamb, but he spoke like a dragon. He exercised all the authority of the first beast on his behalf, and made the earth and its inhabitants worship the first beast, whose fatal wound had been healed. And he performed great and miraculous signs, even causing fire to come down from heaven to earth in full view of men. Because of the signs he was given power to do on behalf of the first beast, he deceived the inhabitants of the earth. He ordered them to set up an image in honor of the beast who was wounded by the sword and yet lived. He was given power to give breath to the image of the first beast, so that it could speak and cause all who refused to worship the image to be killed. He also forced everyone, small and great, rich and poor, free and slave, to receive a mark on his right hand or on his forehead, so that no one could buy or sell unless he had the mark, which is the name of the beast or the number of his name. 
This calls for wisdom. If anyone has insight, let him calculate the number of the beast, for it is man's number. His number is 666.  Revelation 13:11-18

The "other" beast is the False Prophet, made clear in Revelation 19:20.

But the beast was captured, and with him the false prophet who had performed the miraculous signs on his behalf. With these signs he had deluded those who had received the mark of the beast and worshiped his image. The two of them were thrown alive into the fiery lake of burning sulfur.  Revelation 19:20

Beasts so far have been kingdoms, so this is a smaller kingdom or a specific rulership or branch of that kingdom.

Maybe it’s the Pharisees, Jewish religious leaders, who worked with the Beast (Rome) to bring about the death of Christ.  They “exercised authority” and brought Christ to death.  Maybe they are the Priests of Emperor worship.  However, a later vision seems to point the Pharisees to another image (the prostitute).

The False Prophet draws inspiration and power from the first beast.  He's a deceiver, a speaker, an enforcer. He worships/works closely the first beast.

John gives a clue and says the False Prophet can be identified by number 666.  The number points to Nero.  See

Nero was a spokesperson for Rome, a corrupt leader by Roman standards and a persecutor of Christians.  He blamed Christians for a fire in Rome and went crazy, delusional, believing himself to be a great and powerful god.