Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain and let cool enough to handle, 10 to 15 minutes. Cut into cubes.
Mix mayonnaise, celery, onion, vinegar, mustard, salt, and pepper together in a large bowl. Add potatoes and mix to combine. Stir in eggs and sprinkle with paprika.
You can use white potatoes instead of red, salad dressing instead of mayonnaise, and cider vinegar instead of white, if preferred.
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