Start 2 pots of water boiling (one for eggs and one for potatoes).
Once the water is boiling, add the eggs to one pot and potatoes to the other. Let the eggs cook for 15 minutes and remove them to an ice bath (half water half ice). Let the potatoes cook for 25 minutes and then drain in colander. Let both rest for 1 hour.
Cut potatoes in half (or quarters) and add to large bowl. Add celery, dill, pickle relish, one teaspoon salt, and one teaspoon pepper to bowl.
Peel each egg, cut in half and remove yolks. Put yolks in a small bowl and break up with a fork. Cut up egg whites and add to potatoes.
Add remaining salt and pepper, mayo, pickle juice and paprika to egg yolks. Stir to combine (it will be chunky, make as smooth as you like). Pour over potato mixture. Toss to coat.
Serve right away or store in an air tight container in the refrigerator for up to 4 days.