Peel the potatoes and cut them into 1 1/2-inch chunks. Put the potatoes in a pot and add water to cover them by about 2 inches. Salt the water generously. Cover the pot and set it over high heat. Bring the water to a boil, then add the eggs. Reduce the heat to a brisk simmer and cook, covered, until the potatoes can just be pierced by a fork, about 15 minutes.

With a slotted spoon, remove the eggs from the pot and set them aside. Drain the potatoes and place them in a large bowl. Rinse the eggs under cold running water until cool enough to handle. Peel and chop 2 of the eggs and add them to the potatoes. Add the onion, pimento, and relish to the potatoes.

In a small bowl, mix together the mayonnaise and mustard. Spoon over the potato salad, season with salt and pepper, and mix gently.

Peel the remaining egg and slice it, placing the slices on top of the potato salad. Sprinkle with the paprika.

Serve immediately or cover with plastic wrap and refrigerate for up to 4 hours. Serve chilled or at room temperature.