Place potatoes into a large pot, cover with salted water, and bring to a boil. Reduce heat and simmer 15-20 minutes or until tender. Do not overcook!
Drain and return to pot to dry.
Place eggs medium pot and cover with cold salted water, bring to boil. Reduce heat to simmer for 11 minutes, then drain and immediately rinse with cold water. Crack and peel under cold running water.
Allow eggs to cool and chop.
Dice pickles, onion, and celery.
In a bowl mix together mayonnaise, pickles, hard boiled eggs, onion, celery, mustard, vinegar, salt and pepper.
Pour sauce over potatoes and gently turn over potatoes to coat.
Chill in refrigerator for several hours or overnight before serving.