I had to deal with that issue last week and it got me searching for information about keeping potatoes from sprouting because I hate to buy them in small quantities. Whilst doing that research I came across a tip which I'm yet to use but which I believe can be helpful should the need to keep potatoes from sprouting ever arise. If you're an Apple-eater then this will be good news for you. Storing potatoes and apples together will help stop your potatoes from sprouting. It's believed that apples produce some gas which solve your potato-sprouting problem. I don't know if this works so if you've tired it — does it work?
It does work. But you should also know that the same gas that keeps the potatoes from sprouting... and also from getting soft as quickly (an added bonus)... will also cause other fruit to ripen more quickly. This is most obvious when placed in a bowl with bananas. They may look pretty in the fruit bowl with the other fruit, but it is best not to store them there. Also, a cool dark place for both apples and potatoes is best. There are even some commercial made potato bins out there you can use for that. They are usually made of wood to block the light. Mine is homemade, tall with three bins separated by fine wire mesh. It keeps fruit and veggies separate but lets the gas from the apples pass through the mesh. We keep apples, potatoes and onions in the three different bins. I am not sure if the apples affect the onions in any way... but my parents and grand-parents always kept them together... so I do too! They never knew about the gas from the apples but knew to keep them with the potatoes and for some reason with the onions... so I just do too.
I have also heard of the apple trick but have not tried it. I actually completely disagree with keeping your potatoes in a cool, dark place. I used to keep my potatoes in a kitchen drawer but they would start to sprout after just a few days. I moved them to the kitchen counter (not pretty to look at but whatever) and now it takes a few weeks for them to sprout or go soft. I also don't like room temperature apples so I keep those in the fridge so I can eat them cold and crisp. Yum!