Why my 2013 Prius exhaust gas smell like rotten eggs

Did you inadvertently fuel-up with leaded gasoline? That is the symptom of a lead-fouled catalytic converter.

 

Miles or kilometres?

 

Have you been eating a large amount of beans?

 

"Rotten Egg" smell is characteristic of sulphur - which doesn't belong in gasoline.

Switch brands and see if the smell goes away.

 

Rotten eggs smell comes from mouth more often than cars.
I am not sure how is gasoline quality in Srilanka? Are you using Leaded gasoline? One time leaded gas will ruin catalytic converter instantly.
However, bad catalytic converter always throw a code P0420, always. Very often the code came although it is still good enough and may pass smoke test. Prius catalytic converter effeciency standard is higher than older cars.
If the smell is when you just start the car less than 15 minutes, that's normal.

 

Rotten eggs have the very distinctive smell of hydrogen sulfide, H₂S, which the human nose is very sensitive to, and can smell at really low concentrations.

Even low-sulfur gasoline has some sulfur in it, so there will be some sulfur compounds in the exhaust. Under some conditions, the catalytic converter can convert those into H₂S and make the bad smell. That happens when the conditions in the converter are "reducing"—lacking in oxygen—as when the mixture feeding the engine is especially rich. These articles give some more detail on what's going on:

Can NH3 or H2S Be Formed in a Three-Way Catalyst?
The three-way catalytic converter - OpenLearn - Open University

it might be worth checking for any other signs of the engine mixture being unusually rich.

The ECM does test for catalytic converter performance, setting the P0420 code if the test fails, but the test it uses tests something different, the converter's oxygen storage capacity. mr_guy_mann gave a good description of that test here.

The production of H₂S doesn't seem to necessarily mean the converter is bad; even a good converter can produce the stuff, depending on its temperature and what is coming in.

 

This makes a lot of sense. Many years ago, we had a Ford Escort that had a recall on the throttle body because of a sulfur smell. Apparently, it was running rich. Ours didn't have the smell and it ran fine, but of course we let them replace it anyway.

 

Zombie tread brought back to life...

Bad gas and/or bad fuel mixture (too rich) - possibly very dirty air filter. Some cars has a bypass air intake door, to prevent choking-off the engine (VW). You'll also get this smell, following large SUVs up the mountain - while they're gunning the engine to pass you.

Hopefully, Sri Lanka doesn't have very restrictive smog laws like our CARB states - because if he is cooking the CAT, It's going to be an expensive repair.

 

The thread also starts with "I put it in park and rev up ,and after some time ...", which is not a very common operating condition for a Prius, and might not be one they optimized the catalytic converter for.