Gear inch/ratio question

mashton I was idly thinking about skid patches last night on the way home. Although having a prime number sprocket is good for getting lots of patches, it ain't perfect. For example, running 51 x 17 only gives 3 skid spots. However, a prime number toothed chain ring would always give loads of spots.

So, why can't you get a 47 tooth chain ring which would always give 47 spots, I think?

No it is the denominator that tells you how many skid patches you have. A prime chainring would mean you would have as many skid patches as teeth on your rear cog. Or twice if you skid with both feet.