hi Dave and welcome to GoY, are you sure it is centipedes eating your potatoes? Far more likely to be little black slugs. Generally centipedes feed on soil-dwelling mites, insects, insect larvae, baby snails, and slugs.

welcome to GoY from me too.
Centipedes are carnivores so not likely them. could be millipedes but again I agree its more likely to be slugs.

I think you have wireworms that are eating you potatoes. There is very little you can do. I would seem that the only remedy is not to plant potatoes on the ground for about 4 years. Perhaps some other crop might not be so badly affected. There are some varieties of potato which are supposed to have some resistance. You can Google for the varieties. All insecticides which were used seem to be banned now.