Peel potatoes and cut into ¾ inch cubes
Add potatoes to a pot, cover with water by about one inch and add a pinch of salt
Bring water to a boil, then reduce to a simmer
Cook until potatoes are just tender, 8-12 minutes
Combine sugar, salt and pepper in a large mixing bowl; stir to blend. Add warm cooked potatoes and mix gently.
In a small bowl combine mayonnaise, mustard and vinegar; stir until smooth.
Add mayonnaise mixture to potatoes and mix gently.
Add eggs, celery, onion and pimientos to potato mixture; mix just until all ingredients are coated.
Refrigerate, covered, several hours or overnight.