Place potatoes in a large saucepot and add enough water to cover by at least 1 inch. Generously salt the water, and bring potatoes to a boil. Reduce heat to medium-low and simmer until potatoes are tender. Remove from heat; drain and cool completely.
In a large bowl, combine chopped egg, mayonnaise, pickle, and onion. Add potatoes and cucumbers to the egg mixture, and toss until potatoes are well-coated. Adjust salt and pepper as needed. Best served chilled.