I learned to keep seed potatoes a warm dark place inside the house for a whole month until eyes grow 2" long sprouts. Then slice potatoes in 1" pieces with 1 or more eyes on each piece. Let cuttings set for several days to scab over then plant & cover cutting with 1" of soil, with the sprout sticking up 1" above the soil. Within a week there are good size leaves and a month later a 24" tall plants with blossoms. Blossoms indicate new potatoes are starting to grow. Potatoes are a 4 month crop.
Another interesting thing, potatoes do not all produce 2" long sprouts at the same speed. Soon as a few potatoes makes 2" sprouts make cutting & plant them first. Next group of potatoes with 2" eye sprouts cut & plant them next & so on. Soon you have a full row of plants all planted at different times. Harvest will be the first cuttings planted then second an third & so on.
Next garden season no more long 40 ft potato rows I am doing a potato patch to save space. Last year was 2 rows side by side 40 ft long. This coming spring 6 rows side by side 10 ft long. So far my experience growing potatoes is 1 new potato per eye. I will plant 6 eyes in each spot spaced 6" apart with row spacing 6" apart in a patch 10 ft long. 6x6x20 = 720 plants = 720 potatoes.
I am planting onions in a patch too in the same wide row with potatoes, same width but 10 ft long row this will = 240 onions.
15 years ago I planted peppers very close together so plants would shade each other from hot TN sun, I had the best crop of pepper ever, I want to try that again. Plant pepper plants 18" apart in 2 rows 18" apart for 10 ft.
20 ft of potatoes, 10 ft of onions, 10 ft of peppers, all in the same 3 ft wide row 40 ft long. Grouping these plants close together instead of 3 ft row spacing will save a lot of garden space. What ever is planted next to potatoes needs to be gone in 3 months because potatoes plants tend to take up a lot of space the last month of their life.