Are these eggs rotten? I have a carton of fresh eggs here. They don't expire until this time next month. They don't float in a large bowl of water. But many of these ones after being hard boiled have a very strong sulfur smell.

So i looked it up but now i am confused. Some say that smell is a normal reaction that occurs when sulfur reacts to the heat when being boiled. And others say that hard boiled eggs that are rotten have a very distinct and disgusting smell; a smell of sulfur.

So which is it? Are my (very strong) sulfur-smelling eggs rotten or is the smell only caused by the sulfur reacting to the heat?

Right now Id be more inclined to say that the eggs are rotten or that there's something wrong with them, simply because this smell is rare when i make eggs - and i always make my eggs the same way and heat them for the same amount of time.
What you're describing sounds normal to me. It's the result of overcooking them. The eggs themselves were fine. At a guess, you unknowingly messed up the timing for the particular batch described here (alternatively, the eggs may have been smaller than usual). 

Over cooking hard boiled eggs will result in the smell you identified (and also cause the exterior of the yolk to turn green). 

Further information: http://io9.com/when-you-overcook-eggs-you-turn-them-into-chemical-wea-1682497376