Raw potatoes will last from 2 to 3 months in the refrigerator because keeping the potatoes in a dark cold place such as the refrigerator keeps the potatoes from going bad.
When potatoes are left out at room temperature in the sunlight they typically last 1 to 2 weeks before going bad and if you freeze the potatoes they will last up to a year.
I keep potatoes out at room temperature that I'm gonna use within a week or two and if I'm not gonna be using the potatoes within 2 weeks I refrigerate them to make them last longer.
Sometimes I buy potatoes on sale and then freeze some extras while keeping some in the refrigerator to make them last longer.
Bad potatoes will begin to get mushy and have a bad smell to them and should be thrown out.