Boil the potatoes in salted water until tender, about 20 minutes.
Drain and let them cool slightly before peeling.
Pass the potatoes through a ricer or mash them until smooth.
In a mixing bowl, combine the mashed potatoes, flour, and salt.
Add the egg and mix until a dough forms.
On a floured surface, knead the dough gently until smooth.
Divide the dough into 4 pieces and roll each into a rope, about 1/2 inch thick.
Cut the ropes into 1-inch pieces to form the gnocchi.
Use a fork to press each piece lightly to create ridges.
Bring a large pot of salted water to boil and cook the gnocchi until they float, about 2-3 minutes.