Short answer: It depends on the condition of the potato.
Some sprouted potatoes can be eaten after the sprouts are removed. Others should be thrown away. The sections below explain how to tell the difference, based on the condition of the potato.
When it can be eaten
According to Michigan State University Extension and North Carolina Extension, as reported by Iowa State University Extension and Outreach:
- Removing the sprouts allows safe consumption of the rest of the potato as long as the potatoes are firm, not soft or shriveled, and the sprouts are small. Most of the nutrients are still intact.
- Potatoes that are firm and show only small sprouts at the eye and/or skin-deep greening can be eaten if the entire sprout and any green-tinged parts are cut away.
When to throw it away
- If the sprouts are long (1 inch or more) and the potato has shriveled, it should be tossed.
- If more extensive greening occurs into the tuber, throw the tuber away. Never eat tubers that are green beneath the skin.
- If there is extensive sprout growth, shriveling, and deep green within the tuber, the potatoes should be tossed.
Why sprouts and green skin matter
Potatoes naturally contain two glycoalkaloids — natural plant compounds — called solanine and chaconine.
Glycoalkaloids are found throughout the tuber, but in highest concentration in the leaves, flowers, sprouts, green skin, and the area around the potato's eyes. The lowest concentration is in the flesh.
In normal potatoes the concentrations are small, slightly higher in a thin layer immediately under the skin and around the eyes. Peeling potatoes and removing the eyes reduces the presence of the compounds.
The concentration in sprouts is much higher and can be high enough to be toxic to humans. The more potatoes sprout, the greater the presence of glycoalkaloids in both the sprout and the potato itself.
High concentrations give potatoes an unpleasant, bitter taste and can lead to headaches, vomiting, and other digestive issues.
Green-skinned potatoes have been exposed to too much light. Light causes the potato to produce chlorophyll and activates the skin cells to produce solanine, which has a bitter taste and is an irritant to the digestive system.
Peeling the potato and cutting out the green portions eliminates most of the toxin.
Cooking does not fix it
Cooking does NOT destroy glycoalkaloid compounds.
That means you cannot rely on cooking to make a potato that should be tossed safe to eat. Use the condition checks above instead.
Storing potatoes so they last
Store potatoes in a place that is cool (45–50 degrees Fahrenheit), dark, dry, and well ventilated. Kept in these conditions, potatoes will likely last up to three months or longer.
At room temperature, potatoes last about 2 weeks.
A cellar or cool basement is ideal. Keep potatoes away from appliances that give off heat and from any light. Potatoes to be used soon can be stored in a cupboard or pantry in a paper bag.
Do not store potatoes in the fridge: cold temperatures turn the starches into sugars, making potatoes sweeter and making them cook dark.
Do not store potatoes with onions: onions produce ethylene gas, which causes potatoes to spoil prematurely. The high moisture content of potatoes can cause onions to turn brown and rot.
For more food storage questions, the source article names the FoodKeeper — produced by the Food Marketing Institute at Cornell University in conjunction with the USDA — as a further resource.