Leave in potatoes?

I didn't think to leave any bits of plant and pulled out the top layer of potatoes and green/yellow half dead plant. I've harvested a fair few but want to save some for later. Should I leave the rest of the potatoes in the container well covered over with compost or will they rot?

 

You'll find out in months to come, if you forget about them 

DD did explain that-- as you are not leaving them in the ground they will be safe from slug attack