From a science-based approach, here are three sources from Dr Linda Chalker-Scott from Washington State University Extension that will give you more information. Note that she's approaching these topics from an urban gardening (in the ground, not in pots) perspective.
On Phosphorus in the soil
On organic material to soil ratios
On foliar kelp extracts. Note ...
So going by the Triple Mix method. 1/3 Top Soil, 1/3 Compost Manure, 1/3 Peat Moss.
So now I know a 1:1 ratio of compost manure and Top Soil is what's needed.
Now to figure out nitrogen and Phosphorus.
I think I understand potassium, it makes the soil less acidic.
Potatoes can be useful as the first crop on previously uncultivated ground, but probably not for the reason you are hoping.
The main benefit is that if you grow them the traditional way in earthed up rows, you get to dig most of the ground three (or maybe four) times in the growing season while still getting a crop: once when you plant them, once or twice ...