Basically, we have several references to the number four:

"Judah" is the fourth son of Leah and we are told that his name means: "to praise, or honor, God".
In the story about the burial of Sarah we are told that: "Kiryat Arba", which is Hebrew for: "the fourth city", and is located nearby the city of: "Hebron" which in English means: "alliance".
In the same story about Sarah’s burial, we are told that Abraham (his new name) purchases a field and a cave for her final resting place and pays four hundred shekels in silver for this land.
In the story of Noah we saw that it rained for forty days and forty nights and then, later on, we shall see that the Israelites will be forced to wander in the desert for forty years.
When Esau comes to meet his brother Jacob and invite him to live in the new lands where he has settled, he brings with him four hundred men.
When David attacks the Amalikites in order to recapture his goods and people, four hundred Amalikites escape on camels.

Metaphors in the Torah: "Lech Lecha" part 2: Abraham and Alchemy