If I purchased a 50 lb box of potatoes how long would they stay good if stored in proper conditions?

If stored at 45-48°F with 95% humidity the potatoes will last quite some time, potentially months. Most people cannot make arrangements to store them under those conditions. Store in the dark, in a cool location and you should be able to have them stay fresh for a couple of weeks. The potato is about 80% water, so high humidity really helps retain the moisture. Above 55°F the potato will start to shrink and is more susceptible to sprouting.