1. Combine ginger, sugar and water in a small saucepan over medium heat. Bring to a simmer and stir occasionally. Decrease heat to low and continue simmering for 25 minutes. Remove from heat and let cool.  Discard ginger.
2. Add papaya, 2 cups water and lime juice to a blender container. Blend until smooth.
3. Add remaining 2 cups water to a serving pitcher, stir in ginger syrup and papaya mixture.  Serve cold or over ice.