Originally Posted by Richard Kennedy
Close, but not quite the full story.
Just because 17 is prime doesn't mean you'll get 17 skid spots. Consider the gear 51x17. 51/17=3 , so assuming you skid with your pedals in the same place each time you'd only get 3 skid spots. What you're looking for are a ring and sprocket combination which are, technically speaking, relatively coprime. That means the 2 numbers have no common factors.
17 would be a good sprocket to use but, as already shown, you'd have to avoid the 51 ring (3x17) and the 34 ring (2x17).
There are plenty to choose from. eg. any odd size chainring with a 16 sprocket.
Having said all that, I tend to agree with those who've argued that you really don't want to be skidding on the road in the first place. I've ridden fixed on the road for 15+years, if you're in a situation where you need to skid then you're in trouble!
This doesn't belong in this forum but since there have now been two misinformative posts on the topic it deserves to be pointed out. 51/17 gives you 1 skid patch. Since the every time the pedal is in skidding position the wheel is in the same one. To calculate otherwise you find the largest common factor of the CR and cog and divide the cog by that number. If you have a prime chainring then you will have exactly as many skid spots as you do teeth on the cog.
If you actually care about this which there is no reason anyone in the track forum should do a search over in ss/fg.