What was the primary intention of the gospels writers?

The gospels are the heart of scripture, because all of Scripture testifies to Christ. I think of it this way, the Old Testament sets the stage for the gospels, revealing God's character, our sin nature, and pre-figuring Christ's redemptive work. The rest of the New Testament (Acts, the epistles, Revelation, etc.) explain the implications of the Gospels. Jesus said that all Scripture testifies to Him (John 5:39), Scripture is one great story, with one great hero and His name is Jesus