Why does my 1 month olds fart stink so bad. I breastfeed.?

Stinky farts. The answer as to why any fart stinks it is because of the bacteria present in the colon and how they metabolize sugar and fibers, which create gas. The common rotten egg odor is due to hydrogen sulfide gas. In babies the thing to remember is that they are changing from a state (in the uterus) where they had no bacteria at all to being totally full of hundreds of kinds of normal germs in the colon.
Stinky Gas. This is completely normal! Small babies can create unbelievably stinky gas!