Clean potatoes with water and cut into 1-inch pieces. Place in a large pot and will with cold water so that water covers all potatoes by 1 inch. Add a 1½ teaspoon of salt to the water. Heat on high and bring to a boil.
Reduce heat. Cook 15 minutes or until potatoes are nice and tender. Use a fork to feel tenderness.
Next, make the dressing. In a medium bowl combine the mayonnaise, mustard, vinegar, paprika, relish, ½ teaspoon salt, and pepper. Stir until combined and smooth. Set aside.
Drain and let the potatoes cool. This will help the potatoes keep their shape.
In large mixing bowl, add potatoes, celery, and onion to the mayonnaise mixture. Fold in the chopped eggs. Sprinkle paprika on top.