Fill a medium size pot with water. Bring to a boil. Lower to a simmer. Slowly lower eggs into water. Cook for 15 minutes. Drain water and run cold water over eggs. Place eggs in refrigerator.
Scrub potatoes. Add to large pot filled with water. Bring to a boil.
Cook potatoes 20-25 minutes or until potatoes are crisp tender.
When potatoes are done, drain water. Add cold water. Repeat. The skins should easily come off with a little peeling. Remove as much skin as possible (you don't have to get all of it).
Place potatoes in refrigerator with eggs.
While eggs and potatoes are cooling, chop celery, dice onion, and grate radish. Place in a large bowl.
After eggs are cool, peel. Slice open and remove all the yolks.
Mash the egg yolks with a fork. Add mayonnaise, mustard, sweet pickle relish, salt, & pepper. Mix/whip until well combined and egg yolks are completely dissolved.
Chop egg whites.
After potatoes are cool, chop.
Mix egg whites, potatoes, celery, green onion, and radish in a large bowl.
Pour dressing over mixture. Stir WELL to mix all ingredients.
Let chill at least 1 hour before serving (preferably 3+ hours).