From the Agriculture and Horticulture Development Board:
"Q: Where should I store them?
A: You need to keep your potatoes in a dry, dark place. Exposure to light or moisture can bring on rotting in the skin. You’ll also need to allow your spuds to be well-ventilated so avoid any air tight containers or spots – a netted bag or wicker basket should do the trick. Be sure your potatoes are kept in cool conditions as it increases storage length. Kitchen cupboards or cellars are the ideal location as they tend to tick most of these boxes.
Q: How long will they last?
A: Storing your potatoes in the correct way should see them lasting for several months, be sure to keep checking up on them as any rotting can spread if they are close in contact with each other. If you do spot any signs then you may need to throw them out. There are several ways to further elongate the lifetime of your spud! If you place your potatoes in a dark place on top of newspaper at a slightly warmer temperature the skin will thicken making it less prone to bruising and rotting"
Source:
https://www.lovepotatoes.co.uk/hints-and-tips/how-to-store-potatoes/