I am pondering the minimal conditions for growing potatoes.
What type of soil, nutrients and space would it necessitate?
All you need is soil, then put potatoes on top of that, then put hay, or wood chips thick enough to cover the plants. Occasional watering is necessary.
A cultivated bed, double dug down at least 12 inches, smoothed down and then firmed by jumping up and down on a piece of plywood. Add shallow trenches around the base of the 'raised' beds which will easily be at least 1 foot high. Need to know what kind of soil and what compost you've access to. Acid soil; 5.5 -6. That is the toughest to amend the soil unless you already have this soil pH. Where is it that you live? Have you ever done a pH test of your soil? There are ways to lower the pH but they are temporary and only minute changes of pH. They help, yes they do. They are always in the form of a sulfur compound.
Go to Potato Gardens on the internet. They grow certified potatoes in Colorado. You can also grow potatoes in pots using a cage and straw and growing vertically. Best fertilizer is one with even numbers such as 5-5-5. I always get my seed potatoes from this company. The owner's son is a professional in the soil world and they can educate you about soil for potatoes. Very cool mom and pop operation.
We need to know what you've got available for soil, zone and how much you know about growing vegetables, potatoes, greens...