Cook the potatoes in salted, boiling water for 15 minutes, until tender. Drain well and return to the pan, set it over a low heat and dry the potatoes for 1-2 minutes.
Mash the potatoes until smooth, then gradually stir in the eggs and salt. Work in enough flour to form a soft dough.
Break off small pieces for the dough and roll into balls, using floured hands. Press the back of a fork into each ball to make indentations. Repeat until all the dough has been used. Leave the gnocchi to rest for 15-20 minutes before cooking.
Bring a large pan of water to a gentle boil. Add the gnocchi, about 10 at a time, and cook for 3-4 minutes, or until they float to the surface. Drain thoroughly and serve as soon as the gnocchi have been cooked.