Pilot DAR, your comments are of course valid but not the whole story. I've given a description of many priming installations that are problematic. The accelerator pump also provides fuel downstream from the carburettor. As to both engine and carburettor fires I've seen too many and due to over-priming using the installed primer. Whatever the technique used if the engine doesn't start then stop after 3 - 4 rotations. Consider why the engine failed to start. It might have nothing to do with the fuel/air mixture. Don't keep turning and priming although I have seen this advised in some POH. If the engine (exhaust) is hot you have a high chance of an exhaust fire from over priming.