Place the potatoes in a large pot and add enough salted water to cover by 1-inch. Bring to a boil over high heat. Reduce the heat to medium-low and simmer until tender, but not mushy, about 20 minutes. Pour out most of the water and place the pot in the sink. Run cold water over the potatoes for about 2 minutes, or until cool enough to handle. Drain well.

Peel the potatoes and cut them into 1/2-inch cubes. Place in a large bowl. Chop 4 hard-cooked eggs and add to the potatoes, along with the red onion, green pepper, and celery. Sprinkle with the celery seed. Gradually stir in the mayonnaise, mustard, and relish (wear rubber or plastic gloves and use your hands, if you wish), being careful not to smash the potatoes. Season with salt and pepper to taste. Transfer to a large serving bowl. Slice the 2 remaining hard-cooked eggs. Arrange the slices on top of the salad and sprinkle with paprika. Serve immediately, or cool, cover tightly with plastic wrap, and refrigerate until chilled, at least 2 hours.

(Note: For a potato salad with a kick, add 2 seeded and minced jalapeno peppers.)