The shelf life of potatoes is 5 weeks and after 5 weeks the potatoes will go bad and start to smell bad.
If you want to keep the potatoes longer store the potatoes in a cool dark place or in the refrigerator.
The potatoes will keep in the refrigerator for 4 months before they spoil and start to smell.
If you want to keep the potatoes longer than 4 months you can freeze them but they will become soggy once you freeze the whole potatoes.
I will sometimes freeze extra potatoes whole and use them in soups and stews where the sogginess of the potatoes when thawed is not a problem.
For fresh potatoes it's best to buy them fresh and then eat them within the month.
Or cut the potatoes up to make fries and then blanch the cut up potatoes and freeze them so they will always be available and ready to deep fry.