I tried to grow potatoes when I first moved here, and they just turned black and perished, I gave up trying to grow them in the soil as it seemed infested with some dreaded potato disease. But many times I have had potatoes volunteer in my lazy compost piles, and got some very clean and lovely potatoes from them!
Treat yourself to a shrimp ring, and toss the tails in your compost to prevent potato scab.
One year I also planted potatoes deliberately in an old compost pile... they grew well but my harvest was not as good - marauding pests maybe slugs? got at them before they were dug. I don't know if that is because it was an older compost pile, but was not a problem when they volunteered from the peelings I had tossed out.
Also if there is any heat left in the pile just now, then they may have a better chance against that bit of frost. Lucky you with potatoes growing in January!!
