Bring potatoes to a boil in a large pot of cold water that's been liberally salted. Reduce the heat to medium high or a lightly rolling boil and cook for 10 to 15 minutes or until the potatoes are easily pierced with a pairing knife. Drain and let cool until just able to handle.
Peel the skins from the potatoes and cut into large diced pieces. Transfer the warm potatoes to a large mixing bowl and sprinkle with the white vinegar and stir. Allow the potatoes to cool, about 15 minutes. Add the celery and green onions. Chop 4 of the hard boiled eggs and add to the potato mixture.
In a medium bowl, mix the mayonnaise, yellow mustard, celery seed, salt, and pepper. Mix well into the potato mixture and season with more salt and pepper if needed. Sprinkle with paprika if desired. Chill for at least an hour or overnight before serving.