Place diced potatoes into a large pot. Cover with cold water and season liberally with salt. Bring a a boil; boil until potatoes can be easily pierced with a fork, about 10 minutes (depending on the size of your potato pieces). Drain potatoes; set aside to cool.

Peel cucumbers and slice in half lengthwise. Use a spoon to scoop out the seeds, then dice and place in the biggest bowl you have. Add the rest of the ingredients; stir to combine. Fold in the cooled potatoes. Cover and chill for several hours or overnight to allow the flavors to meld.