The shelf life of potatoes is about 1 week when left out on the counter or in the pantry.
Storing the potatoes in a cool dark place such as in a basement or in a dark cupboard that stays cool can help extend the shelf life of the potatoes.
When it comes to potatoes though it's best to only purchase enough potatoes that you can reasonably use up within 1 to 2 weeks.
I've had potatoes last up to 2 weeks before but sometimes the potatoes have gone bad within 8 days of purchasing them.
Most times I use the potatoes up before 1 to 2 weeks anyway but if not I will cut the potatoes up and blanch them and after blanching the potatoes I freeze them.
When the potatoes are blanched and frozen after cutting them up into fries they will last for around 6 months.