In Genesis 3 sin enters the world. In Genesis 4 sin spreads. In the first half of the chapter, Cain sins, and we see that Adam and Eve's sin is not only theirs but their family's. In the second half of the chapter, Lamech sins, and we see that Adam and Eve's sin is not only their family's but their descendants'.
Here's how Lamech describes his sin.
Lamech said to his wives: "Adah and Zillah, hear my voice; you wives of Lamech, listen to what I say: I have killed a man for wounding me, a young man for striking me. If Cain's revenge is sevenfold, then Lamech's is seventy-sevenfold." (Gen 4:23-24)
According to Lamech, Cain's sinful revenge was sevenfold. Lamech's sinful revenge was not seven but seventy-seven. Where have I heard something like this before . . .
Then Peter came up and said to him, "Lord, how often will my brother sin against me, and I forgive him? As many as seven times?" Jesus said to him, "I do not say to you seven times, but seventy times seven (or: seventy-seven). (Matt 18:21-22)
Genesis 3 and 4 and the many chapters following tell the story of sin infecting God's world. The coming of Jesus is the story of what God has done to disinfect the world, to cleanse it, to make it new. Good Jew that he is, Peter covers all his bases and chooses the number of completion, seven, as what is surely going above and beyond the call of duty in forgiving another. And surely Jesus had Gen 4 in mind when he responded to Peter. Vengeance, multiplied sevenfold and then to seventy, has been overturned in Jesus' Kingdom ethic of forgiveness, multiplied sevenfold and then to seventy--no, to seventy times seven.
The way to live in such a radically forgiving way? Jesus himself would provide it. Not in his teaching, but in his blood. Oswald Chambers rightly said that if Jesus came mainly to teach us, then all he did was tantalize us by erecting a standard we cannot come anywhere near. But he did not come only to teach us but to make us what he teaches we should be.
We forgive seventy times seven because God has forgiven us, in Christ, seventy thousand times seven thousand.