Hi Larry, I'm surprised no one answer your question yet.
The rule potato growers use, is the longer you leave them in the ground, the longer they will last in storage. (I'd be sure not to let them stay in the ground through heavy saturating rains.) Harvest weeks after the tops die back.
Two of our kennebec plants died (while the rest are still green), so we dug those out and ate them. OH they were good too! Good luck with your potatoes.