The Number of the Beast
Revelation 13

Revelation 13:1-2 (TS2009)
And I stood on the sand of the sea. And I saw a beast coming up out of the sea, having seven heads and ten horns, and on his horns ten crowns, and on his heads names of blasphemy. And the beast I saw was like a leopard, and his feet were like the feet of a bear, and his mouth like the mouth of a lion. And the dragon gave him his power, and his throne, and great authority.
In the prophecy about the Woman and the Dragon in Revelation 12 we saw the dragon with seven heads and ten horns in heaven representing Satan and Satan's spiritual power over his last global empire on earth. This beast in Revelation 13 represents Satan's final global empire on earth. The body of this beast coincides with the beasts mentioned in Daniel's Four Beasts: the lion, the bear, the leopard, and the beast with ten horns. Its seven heads are the heads of Daniel's beasts combined, they merged to become one final beast power.
Revelation 13:3 (TS2009)
And I saw one of his heads, as having been slain to death, and his deadly wound was healed. And all the earth marvelled after the beast.
One of these powers will cease to exist or loose its power for a while and then come back into existence or regain its power.
Revelation 13:4-5 (TS2009)
And they worshipped the dragon who gave authority to the beast. And they worshipped the beast, saying, “Who is like the beast? Who is able to fight with him?” And he was given a mouth speaking great matters and blasphemies, and he was given authority to do so forty-two months.
These powers and their leaders will worship Satan. The beast was given amouth speaking great matters and blasphemies. This is a parallel with the little horn of Daniel's Four Beasts. The forty-two months equals "a time and times and half a time" in Daniel 7. In Revelation 12 we learned that "1,260 days" is the period that God's people are nourished or protected. The fact that the same period is reflected in three different ways in different prophecies likely means that this period is literally 3.5 years or 42 months or 1,260 days, and not symbolic or prophetic days, months or years with a different duration.
Revelation 13:6-7 (TS2009)
And he opened his mouth in blasphemies against Elohim, to blaspheme His Name, and His Tent, and those dwelling in the heaven. And it was given to him to fight with the set-apart ones and to overcome them. And authority was given to him over every tribe and tongue and nation.
The beast fights with God's chosen ones on earth and kills them after which they will be taken up into heaven. From the Son of God we know that in the time of the end there will be chosen ones on earth which need to be gathered by His messengers to complete God's Kingdom (Matthew 24:31, Mark 13:27). After these are killed they will complete the government of 144,000 (Revelation 7:4) that will rule together with the Son of God in heaven.
Revelation 13:8 (TS2009)
And all those dwelling on the earth, whose names have not been written in the Book of Life of the slain Lamb, from the foundation of the world shall worship him.
All ungodly people will worship Satan.
Revelation 13:9-10 (TS2009)
If anyone has an ear, let him hear. He who brings into captivity shall go into captivity, he who kills with the sword has to be killed with the sword. Here is the endurance and the belief of the set-apart ones.
See also Jeremiah 15:2, Jeremiah 43:11, Genesis 9:6. In the Old Testament we see for exampleeye for eye, tooth for tooth...(Exodus 21:24). God is righteous and will make all things right. In the Old Testament God's people were kept in Babylonian captivity. During Satan's final global empire on earth God's people will be held in captivity again, but God will protect His people and make things right in the end. God's chosen ones will be persecuted and killed after which they will be taken up into the government in heaven.
The false prophet

Revelation 13:11 (TS2009)
And I saw another beast coming up out of the earth, and he had two horns like a lamb and spoke like a dragon.
This beast comes from the earth, not from the sea like the other beasts. Earth as opposed to sea symbolizes stability (1 Chronicles 16:30-32). Perhaps it means that this beast emerges in a time of relative stability on the earth after the time of chaos as symbolized by the sea from which the final global empire emerges.
In the Scriptures a lamb symbolizes the Messiah. This beast will present itself as the Messiah but it speaks like a dragon. A wolf in sheep's clothing. This is another beast power of Satan. Perhaps it is the false prophet mentioned in Revelation 20.
Revelation 13:12-13 (TS2009)
And he exercises all the authority of the first beast in his presence, and causes the earth and those who dwell in it to worship the first beast, whose deadly wound was healed. And he does great signs, so that he even makes fire come down from the heaven on the earth before men.
In Revelation 19 we read...
Revelation 19:20 (TS2009)
And the beast was seized, and with him the false prophet who worked signs in his presence, by which he led astray those who received the mark of the beast and those who worshipped his image. The two were thrown alive into the lake of fire burning with sulphur.
The eight beast is likely this false prophet from Revelation 19. The false prophet is going to deceive as many people as possible, trying to make them worship false gods.
Fire from heaven is usually related to punishment from God. Sodom and Gomorrah is a good example. Peter warned thatthe present heavens and the earth are treasured up by the same Word, being kept for fire, to a day of judgment and destruction of wicked men.(2 Peter 3:7)
Revelation 13:14 (TS2009)
And he leads astray those dwelling on the earth because of those signs which he was given to do before the beast, saying to those dwelling on the earth to make an image to the beast who was wounded by the sword, yet lived.
The false prophet will deceive the people on earth and will force people to make an idol for worship. This idol is likely related to the image in Nebuchadnezzar's Dream.
Revelation 13:15 (TS2009)
And there was given to him to give spirit to the image of the beast, that the image of the beast should both speak and cause to be killed as many as would not worship the image of the beast.
In Daniel 3 we read that king Nebuchadnezzar ordered all people to worship the image that he made. Those who refused would be killed. Something similar will be done in the time of the end by the false prophet.
Revelation 13:16 (TS2009)
And he causes all, both small and great, and rich and poor, and free and slave, to be given a mark upon their right hand or upon their foreheads,
The hand is often used in regard to an action (Exodus 15:6, Psalms 74:11, 1 Kings 8:15,24). The forehead is often used in regard to a person's belief (Ezekiel 9:4, Revelation 7:3, 1 Kings 8:15,24). A person's belief and actions are related (Deuteronomy 6:8). The mark is directly linked to the worship of Satan. Those who receive the mark made the choice to worship Satan.
Revelation 13:17 (TS2009)
and that no one should be able to buy or sell except he that has the mark or the name of the beast, or the number of his name.
There will be a time when the rulers in Satan's global empire will set up a financial system of slavery which will force people to worship Satan in order to be able to make use of that financial system.
The number of a man

Revelation 13:18 (TS2009)
Here is the wisdom! He who has understanding, let him calculate the number of the beast, for it is the number of a man, and his number is six hundred and sixty six.
Wisdom is inextricably linked to king Solomon. Two other places in the Scriptures wheresix hundred and sixty sixis used are 1 Kings 10 and 2 Chronicles 9. After king Solomon had finished building God's temple he received six hundred and sixty-six talents of gold every year. Around that time he also started breaking God's laws. Perhaps this indicates that gold and material wealth corrupted him. Power corrupts men. Every human king throughout history was more or less corrupt, even those who started as king of God's people eventually became corrupt. During Solomon's reign God broke the covenant that He had made with his father, king David.
Another place in the Scriptures is Ezra 2:13 where God's people are listed who returned from the Babylonian captivity under king Nebuchadnezzar. After the Persians conquered the Babylonian Empire they allowed God's people to return to Jerusalem, even to rebuild the temple. The sons of Adoniqam count six hundred and sixty-six. Interestingly, after God's people started rebuilding the temple his sons are listed again in Nehemiah 7:18 counting six hundred and sixty-seven.
In the Scriptures the number 6 is linked to humans. On the sixth day God created man (Genesis 1). The number 7 is linked to God. On the seventh day God rested (Genesis 2). Man is created by God and is below God. But it seems that man wants to be God himself. Satan deceived Eve by telling her that she could become like God and then Eve deceived Adam (Genesis 3).