Hi Steve, I think there are 3 digits missing from the code you have posted. If you supply the complete code we should be able to tell you your engine's date of manufacture. It is an 8 cubic inch (130 cc) first design generation engine with a horizontal crankshaft, a Pulsa-Jet carburetor, plain main bearings, and a recoil starter.

The fact that it will start if primed but not otherwise, means that the carburetor is not functioning. Fixing this will involve removing the carburetor and fuel tank, still connected together, from the engine, then separating them, cleaning both, and reinstalling.

Here are the B&S instructions for doing the job:
http://recoveryvehicles.tpub.com/TM-5-4240-501-14P/css/TM-5-4240-501-14P_108.htm

However I suggest that you do not undertake a full overhaul of the carburetor at this stage. There are a couple of things that are particularly likely to be the problem, and they are relatively easily checked. If you begin by looking into the fuel tank, you may find there is a lot of garbage on the bottom of it: old grass, and other things that have found their way into the tank during refuelling operations. If you separate the tank from the carburetor, you can then clean out the tank, and inspect the fuel filter screen at the bottom of the longer of the two tubes extending down from the bottom of the carburetor. You may find the fine mesh is crudded up and blocked. Follow the manual's instructions for removing the tube (not the mesh - it has to be cleaned in situ) and cleaning the mesh. (Figure 47). Then clean the metering holes and inspect the needle valve (Figure 50), and check the fuel pump diaphragm (Figure 51). If the diaphragm passes inspection, put the carburetor back together, reattach it to the fuel tank, and put the assembly back on the engine.

By removing the needle valve (to get access to the metering holes) you have lost the mixture adjustment, so when you reinstall it in the carburetor use the "standard" adjustment of 1.5 turns anticlockwise from fully clockwise. Be very gentle when you turn it fully clockwise - just turn it until you feel the presence of the seat, don't "tighten it up". Carburetor tuning instructions are on page 111 (you started on page 108; just keep using the "next" button at the top of the page).

Please come back to us with any questions you have. Feel free to clean out more of the carburetor if you are confident to follow the instructions in the on-line manual - I do not know what experience you have in this kind of work, so I've just covered the most likely sources of your blockage.