Raw unpeeled potatoes will last from 1 month to 2 months as long as you properly store them.
It's best to store the raw potatoes in a cool dark place to help keep them from going bad so quick.
I sometimes will freeze bags of potatoes and then use them in soups, stews etc.
When you peel the potatoes then you need to refrigerate them to make them last longer because when left out the peeled potatoes may only last a day or so.
Even refrigerating the potatoes will help them last longer or keep the potatoes in a basement or cellar that is dark if possible.
The potatoes when kept in a cool dark place will last at least a month or two or even a bit longer.
I usually use my potatoes up before a month anyway so it's never really a problem.