A single large potato is high in potassium, magnesium, iron, copper and manganese. It also contains vitamin C and most B vitamins (27). They contain a little bit of almost every nutrient you need. There are accounts of people living on nothing but potatoes for a long time. They are also one of the most filling foods. When researchers compared the satiety value of different foods, boiled potatoes scored higher than any other food measured (28).
If you allow potatoes to cool after cooking, they also form resistant starch, a fiber-like substance with many powerful health benefits (29).
Potatoes contain a little bit of almost every nutrient you need. They are incredibly filling and can provide large amounts of resistant starch.