So, why can't we store potatoes in the fridge? Well, it's because the cold temperature can actually cause the starches in the potato to convert to sugars, making them sweet and unappetizing. Yeah, not exactly what you want in a potato!
Instead, it's best to store potatoes in a cool, dark place with good ventilation. Think: a pantry or a root cellar. This will help keep them fresh for a longer period of time. Easy peasy, right?