These are supposed to be organic. Do they treat those? They are sprouting very well so maybe they will be ok.(Maybe, I`m fortunate and these were cold stored and not treated.)
Edited to add: If you start by just planting them 1/2 way in the dirt and do not cut them up they should sprout. I think cutting them up makes them prone to rot.
Potatoes that you purchased in the store that were from this year's crop that were not stored properly to break the rest period will sit there and do nothing until maybe you put them somewhere cold in the 50`s for about a month then take them out and plant them outside in the warm weather. Potatoes have a rest period which must be broken before the seed will sprout. Cool temperatures or extremely warm temperatures can break the rest period and allow potatoes to sprout.
It is better to plant certified seed potatoes that have been properly stored to induce sprouting. That way you know they will definitely sprout...but don`t eat them because seed potatoes are frequently chemically treated as well.
