That number is cast into the intake pipe, it is a part number not a serial number.
Remember, you only prime the engine when it is cold. When it is warm, if you prime it you will make it hard to start.
If it was dead cold and you primed it, or warm and you didn't prime it, the engine being a bit hard to start is likely to be due to one of three things: weak spark, poor compression or incorrect air/fuel ratio.
You have concluded that the spark is OK. It might be an idea to check it again occasionally to be sure it always gives an evenly-spaced series of blue sparks when you pull the starter. Erratic ignition indicates a problem, and so does a weedy little red spark rather than a consistent blue one.
You can make a simple compression check by seeing how difficult it is to pull the starter cord, or by using the technique recommended by Briggs and Stratton. When you pull the starter you should feel a considerable resistance every second full turn of the engine - to tell whether it is "normal" you'd have to compare it with another 4 stroke mower (2 strokes feel quite different). The alternative is to do the Briggs trick, which gives clearer results. First and most important, disconnect the spark plug lead, and make sure the lead cannot flop back onto the end of the spark plug while you are not looking. Then rotate the blade plate (put the mower up on blocks, don't tilt it) backwards (opposite to the way it moves when you pull the starter). After you turn it some distance you should feel resistance, and the resistance should be a bit rubbery. It is the pressure of the air in the cylinder, being compressed by the piston as it moves upward in the cylinder. When you have found that point, move the blade plate forward a bit, and then flip the plate in the backward direction with your fingers, so it is moving briskly when it hits the resistance. It should bounce off the compression, and move forward at least a couple of inches on the outside of the blade plate. If it does that, the compression is probably not too awful.
To check whether the mixture is a problem is more difficult, and you do it by the way the engine runs rather than the way it starts.
