Because these are fresh potatoes, how long they last will depend more on how they are stored. For this reason, many stores choose not to have an expiration date added to the packaging. As long as the potatoes are not really soft or breaking down, you should be good to go.
For the best and longest storage possible, you'll want to store your potatoes in a cool, dark place. The optimum storage is 45-55 degrees Fahrenheit, and potatoes store best in the dark. Keeping them this way should allow them to last for several weeks, depending on storage conditions.
Storing them in the refrigerator allows the potatoes' starches to break down into sugars, which may change the flavor of the potatoes, so if you must refrigerate them, use them up within a few weeks to get the best flavor possible!