It typically takes 1 month at about 74° F for seed potatoes in cold storage to break dormancy, that can vary from 2 weeks to 6 weeks depending when commercial growers get potatoes in bags then shipped them to stores for sale.
I buy grocery store potatoes Jan 1st because our local garden supply stores sometimes have no seed potatoes for sale until several weeks past the date seed potatoes should have been planted in my garden.
I place seed potatoes on a large table in a sunny window on the north side of the house. Potatoes need to be in bright shade for eyes to sprout. If dormancy has already been broken potatoes might start sprouting in 2 weeks. If dormancy is not broken it takes 6 weeks for potatoes to start sprouting.
I set potatoes in cardboard tray with eyes pointed at the sunny window. Sprouts will be short stubby things with many root nubs looking for wet soil to grow in.
March 1st is potato planting day in TN but if garden is mud I can not plant, seed potatoes rot in cold mud. Fall I need to remember to till 3" of sawdust into the soil then hill soil up 3" high so there is no mud. If rain is in the forecast I need to wait until soil is dryer. I like to plant seed potatoes sooner than March 15 if possible.
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New potatoes are like tiny jacks that have to lift heavy soil up so seed potatoes can grow larger. 1 new potato does not have much lifting power but 20 new potatoes has a lot of lifting power. Do not be afraid to over crowd seed potatoes.
I do not cut seed potatoes. I plant seed potatoes with a minimum of 5 eyes or more per seed potato. Each eye grows 1 plant and each white color potato will grow 1 lb. of new potatoes. Red potatoes will grow 2 to 4 lbs. of new potatoes for each plant. A white seed potato with 5 plants will grow 5 lbs. of new potatoes. Red seed potato with 5 eyes will grow 10 or more lbs. of new potatoes.
I plant 5, 6, 7, 8 eye seed potatoes 6 inches apart. If I have 2 eye and 3 eye seed potatoes I plant them about 3" apart.
My rows are 30 ft long 32" apart. Till the soil then rake it flat and level. I sprinkle 1 lb. of 15-15-15 fertilizer on each 30 ft row then set seed potatoes on the soil surface in a straight line push seed potato down 1" so half of the potatoes stay above the soil. Rake 3" to 4" of soil over the tops of the seed potatoes. Your soil seldom freezes more than 1" deep 3" of soil protection works good for us.
When green plants are 6" tall sprinkle 1 lb. of 5-20-20 fertilizer on each 30' row, rake soil hill up 3" higher. Every time plants are 6" rake soil up another 3". TN spring weather we have rain 6 days a week March to last week of May. Rain every day will not hurt green plants or new potatoes. If we have odd weather with NOT much rain I use 2 potatoes hills side by side like an irrigation ditch put garden hose in the center and turn it on. Shovel some soil at the ends of the 2 rows to make a dam so irrigation water does not escape.
Rake soil hills up to about 10" high. We often have too much rain it washes my 10" hills down to about 8" or less. Feed each row of plants 1 lb. of 5-20-20 fertilizer every 2 weeks.
When green plants turn yellow stop all water and let plants die.
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If you sprout seed potatoes in the dark you get 100s of spindly stems, this is not the best way to grow seed potatoes but it will work. This year we has crazy hot 85° weather until mid December I had NO place cold to make my seed potatoes go dormant. 74° inside the house was better than 80+ outside in the shed. Soon as we had cold weather my seed potatoes were moved outside but too late now they are trying to grow plants. OH well not much of a big deal seed potatoes will still grow. There is nothing wrong with breaking off all those tall skinny sprouts and forcing the potato to grow new eyes with roots. Eyes with roots gives you a fast start growing green plants.