Some potatoes sold in stores are coated with a solution to prevent sprouting which will either do as said, or if they do sprout will produce few if any potatoes.
How a potato, including genuine seed potatoes, act depends on the variety one plants. I planted about a dozen varieties, almost all on April 1st this year including left over eating potatoes and all have done well.
They are at different stages of development and size.
The one stubborn variety is called Peter Wilcox and they, are pretty much just sitting there, hinting they might sprout out greens if they get a hankering to.
I dug down to them last week and they are just sitting there, not rotting but not much more, although one potato despite not having even sent up any greens had already produced one small potato.
OF the four I planted one is now above ground but I am not sure what I will do with the other three. Maybe dig them up and put them out to chit, or put then in the fridge for a day or two to see if the need that.
As hard as they still are I could just peel them and eat them also.
I put some of the store bought left over eaters in bare spots in the rose garden as I am not sure if I am going to reduce down to just one rose garden but anyway, the soil in that garden, over the years amounts to the best one can possibly make due to amendments and special soil used to plants roses.
The potatoes there are dong EXTREMELY well, so if your sig. other ever has a bare spot in her rose garden, slip a tater in there when she is not looking.