A picture of Manitou potato variety harvested from one plant

The number of potato tubers produced by each potato plant is influenced by agronomy and varietal potential. Correct balanced nutrition is critical in influencing number of tubers per plant. Phosphate, Potassium and Calcium have all been shown to have effects on the total achievable tuber number.

A large number of tubers per hectare will produce a crop of predominantly small sized tubers; ideal for seed potatoes. A relatively low tuber number provides less competition per unit area for nutrients and allows the crop’s energies and resources to be used to produce larger potatoes for the fresh processing market.

https://www.yara.us/crop-nutrition/potato/how-to-increase-potato-tuber-numbers/