Revival and prayer

It seems that major turning points in church history and revival have often been associated with extraordinary times of prayer. We are often exhorted to prayer on that basis. But what is the evidence for this in the Bible? Luke-Acts are famous for their emphasis upon prayer. But until recently, I hadn't noticed how prayer is not just mentioned a lot, but is interwoven into the narrative so that at major turning points prayer is always in the picture.

Here's a list: the coming og John the Baptist (1:13), the birth of Jesus, the temptation, the choosing of the apostles, the sending out of Jesus's followers, prayer before cross, prayer at the cross, Pentecost, the beginning of persecution in Acts 4, the gospel to the Gentiles (Cornelius’s prayer is heard), and the sending out of the missionaries.

It's not just that prayer is mentioned a lot but that the very structure of the story is embedded in prayer. This would seem to indicate that prayer is always associated with every significant work of God. I wouldn't want to say that things happen just because of prayer (God's grace is always prevenient) but that prayer is always 'around' when big things happen! Perhaps we might say that the existence of fervent prayer is itself a demonstration of an extraordinary work of God.