It's essentially an external kidney stone.
You can use various types of acid - sometimes a alternating approach of chlorine bleach (by itself) to kill the biofilm that's exposed and acid (by itself) to remove the "more or less limestone" is beneficial. The biofilm can prevent or slow the acid from getting to the underlying stony material, and it tends to have a layered structure.
Vinegar works, but slowly. Citric acid should work better (it's a stronger acid) but can be harder to find. Muriatic (aka hydrochloric) makes me a bit uncomfortable, personally, but there are commercial toilet cleaners that contain it. Be sure to use gloves and goggles if you opt for the stronger stuff.