Whatever sort of limescale remover I buy it just dribbles away before it gets a chance to dissolve the build up. This has been a lifelong problem of mine, being unable to clean this area. I even bought a pumice stone but its too big to fit under the rim 
I'm even tempted by sprits of salts but I have no ventilation in the bathroom. And surely it would just run down without dissolving anything wouldn't it?