Basically, these are potatoes that have not been treated to prevent sprouting. They are also less likely to have problems with disease. You can plant potatoes from the store, but it’s riskier.
One potato can be cut up and planted in several pieces–just be sure each piece has 2-3 eyes and weighs at least 2 ounces. Set the cut pieces out and allow a crust to form before planting. Otherwise, it will just rot.
