There are different kinds of prayer. There is the prayer of thanksgiving, there is a prayer of petition, where we ask God for something, and there is Contemplative prayer, where we without words, ask God to grant us the Spiritual experience of being one with Him. People often speak of prayer having the power to do things but that is inaccurate. It is God who has power! If I ask God to heal someone and then that person is healed, it is neither I nor my prayer that has done something. It was God in His love, kindness, and power who healed the person. So your answer is, no, prayer does not cure illness but Almighty God in His love, mercy, and goodness who often heals people.