From the extension publications that we reviewed, this is our recommendation for your potatoes.  Yes, you may can red ones.

•  Place harvested potatoes in a warm (60°F to 65°F), well-ventilated area to allow the skin to set and any wounds to heal.
  • Keep them under cover or in the dark, and allow ten days or more for them to cure completely.
• Check over the potatoes, removing any that are soft or shriveled. Eat these ones soon.
• Green skin occurs when potato tubers experience exposure to light. Remove any green areas before cooking potatoes. Do not consume potatoes with extensive green areas.
• Gently brush any dried soil off the tubers, but do not wash them.
• Store in a cool (42°F to 50°F), dark, moist (90% relative humidity) area. This is warmer and more humid than refrigeration. It is also somewhat warmer than a root cellar.
• Most homes do not have a good place for long-term potato storage. An old refrigerator set to a higher than normal temperature, a basement or garage storage space, and a semi-finished attic are possibilities.
• Remove any sprouts from potatoes prior to using them for food. The longer potatoes are in home storage, the more likely they will begin to sprout.
  • Potato sprouts can be toxic and you should not eat them.
• You may can potatoes only if you process them using a pressure-canner.

 The canning information is from this link:
 https://nchfp.uga.edu/how/can_04/potato_white.html

Selecting, Preparing and Canning Vegetables

Potatoes, White - Cubed or Whole

Quantity: An average of 20 pounds is needed per canner load of 7 quarts; an average of 13 pounds is needed per canner load of 9 pints. A bag weighs 50 pounds and yields 18 to 22 quarts – an average of 2½ to 3 pounds per quart.

Quality: Select small to medium-size mature potatoes of ideal quality for cooking. Tubers stored below 45ºF may discolor when canned. Choose potatoes 1 to 2 inches in diameter if they are to be packed whole.

Please read Using Pressure Canners before beginning. If this is your first time canning, it is recommended that you read Principles of Home Canning.

Procedure: Wash and peel potatoes. Place in ascorbic acid solution to prevent darkening. If desired, cut into 1/2-inch cubes. Drain. Cook 2 minutes in boiling water and drain again. For whole potatoes, boil 10 minutes and drain. Add 1 teaspoon of salt per quart to the jar, if desired. Fill jars with hot prepared potatoes, leaving no more than 1-inch headspace. Cover hot potatoes with FRESH boiling water, leaving 1-inch headspace and covering all pieces of potato. (Caution: Do not use the water you cooked the potatoes in; it contains too much starch.)

Adjust lids and process following the recommendations in Table 1 and Table 2.

Table 1. Recommended process time for White Potatoes in a dial-gauge pressure canner. Canner Pressure (PSI) at Altitudes ofStyle of PackJar SizeProcess Time0 - 2,000 ft2,001 - 4,000 ft4,001 - 6,000 ft6,001 - 8,000 ftHotPints35 min11 lb12 lb13 lb14 lbQuarts4011121314

Table 2. Recommended process time for White Potatoes in a weighted-gauge pressure canner. Canner Pressure (PSI) at Altitudes of  Style of PackJar SizeProcess Time0 - 1,000 ftAbove 1,000 ftHotPints35 min10 lb15 lbQuarts401015

This document was adapted from the "Complete Guide to Home Canning," Agriculture Information Bulletin No. 539, USDA, revised 2015.

Reviewed February 2018.