When potatoes are frozen they last longer than non frozen potatoes.
I've kept frozen potatoes in my deep freezer for up to a year without them going bad although they get mushy and are not as good.
But I usually freeze even whole potatoes and then put them frozen into soups and stews or into my slow cooker and then cook them that way.
Then I don't notice the texture and taste change.
If you want to freeze potatoes to use for fries you should blanch the potatoes before freezing them to prevent them from going mushy.
Freezing the potatoes helps keep them from going bad as quick as they would without.
You can also store fresh potatoes that are uncut in a cool dark place.
My grandpa used to grow potatoes and store them under dirt in his basement and they would last a long time that way.