That should be a Tecumseh engine.
IF it has the "Brass Nut" holding the carb bowl on, then that is the MAin Jet.
Clamp off the fuel line and remove the nut. Clean the holes out.
Before reinstalling, I'd unclamp the fuel line for a couple seconds to flush.
Reinstall the nut and mow.

btw....IF YOU HAVE THE BULB TYPE PRIMER AND THE RUBBER IS CRACKING THERE COULD BE AIR GETTING IN THROUGH THE LITTLE CRACKS...JUST PAINT TH LIQUID STYLE SILICON GLUE(NOT CAULK STYLE, THIS IS USE FOR WINDSHIELDS IN AUTO PARTS DEPT) ALL OVER IT SINCE YOU OFTEN HAVE TO REMOVE THE CARBURETOR OR POP OUT A THIN METAL/PLASTIC RING WITH A TINY SCREWDRIVER OR PICK TO REPLACE THE OLD BULB, THIS WILL PUT A NEW COATING OF RUBBERY SILICON RUBBER GUARANTEED TO STOP THE AIR LEAKS AND HARD STARTING OR STALLING AFTER 5 SECONDS.

It's the center bolt as Bill said, without a doubt. It has three orifices to clear: 1 large hole through the bolt just over the head; 1 jet down in the center; and the troublemaker - up at the top of the threads near end of bolt is a tiny hole that's on an angle. Use a pipe cleaner on the large fuel pickup hole; strip the paper off a wire tie and use the wire on the other two. Then blow them out with carburetor cleaner spray.
Tip: Turn the mower up on its right-side wheels (carburetor UP) before loosening the fuel bowl nut. This way the fuel bowl will probably stay on and no fuel will be spilled. When putting the bolt back, don't over-tighten. After installation set the mower down and see if the bowl leaks. Tighten only 1/8 turn at a time until the leak stops. The mower should now run properly. Always use STA-BIL in your gas can every time you get gas. This will most likely make jet cleaning less frequent.

I had this same problem with my 17 year old
Craftsman and after adding 1-1/2 teaspoons (per quart of gas) of Gumout it runs like new. Drain all but a small amount of gas then add the Gumout then fill the tank. Good Luck.

Bill and saxman, you were absolutely right. I cleaned out my brass bolt today and it fixed my stalling problem right away! Thanks!!

Thanks for the tip on the brass bolt. Used a pin on the jet and now it works like new!

Great tips, running just fine now!!!

Just had the same problem. I found a YouTube video showing where the brass bolt is, and sure enough, cleaning out those tiny holes did the trick! Thanks, Bill!

Thanks for info above. Cleaned bolt/jet last year and worked great. Had to do it a couple of more times, last year, but always worked. Replaced gas, etc., so no issues there.
This year, I've done all of the above, but the mower will not remain running. I use starting fuel to get it running, but it will choke out unless I give another squirt of the starting fuel. Then it chokes again, etc. etc......

I'm not very skilled here, but it seems to be some sort of fuel pick up problem, as it will run if I spray the starting fuel. Any ideas?
Thank you!

There are 2 small seals around the plastic emulsion tube in the stem , an improperly sealed bowl or even a head gasket which has started to blow out which could contribute to this. I assume that the fuel is clean and fresh and there is a good flow to the carb. The air filter body must also be installed to the carb in order to prime properly - that is assuming that this is the same mower engine as the OP...