The engine was built on 29 April, 2002. The plant code (51) refers to one of the administrative centers at Briggs' head office in Wauwatosa, Wisconsin, not an engine plant. This seemed to start happening about the time Briggs' China plant opened, and I have never seen or heard of a Briggs engine that actually has the China plant's code (28) on it. I'm not accusing anyone of anything, but I'm not discounting that particular conspiracy theory either.

Here is the Illustrated Parts List:
http://bsintek.basco.com/BriggsDocumentDisplay/18howHXCnfBhU7y.pdf

Here is the Operator's Manual:
http://bsintek.basco.com/BriggsDocumentDisplay/flmrtKX-nfBhU7y.pdf

Note that this is a Pulsa-Prime carburetor, and there is no choke coupled to the speed control. The manual says always start it with the speed control on maximum.

If a Pulsa-Prime carburetor like yours will only run at full speed for 10 seconds, then show signs of running out of fuel, the chances are it took 10 seconds to empty the fuel reservoir in the top of the fuel tank. Since it will run properly at lower speeds, there is a good chance it is suffering from insufficient fuel pump output. I think the first thing to do is to inspect the fuel pump diaphragm.