One thing fixed gear riders have noticed is that if the number of teeth on your chainring and the number of teeth on your rear-cog are relatively prime, then for any given such combination you will maximize the number of skid patches on your tire. This is good because you will have to replace your tire less often.
What's more, you can achieve more versatility by making the number of teeth on the chainring prime. That way, you can have a one or two tooth difference in cog size on the flip-flop, (which will give a greater difference in gear ratio for each side than the same difference in teeth on the chainring,) --and no matter what number of teeth you have on either cog, it will be relatively prime with the front chainring. This is because any number of teeth on the rear-cog will be relatively prime with the (prime) number of teeth on the chainring.
As Stephen Colbert once said to our bow-tie sporting local congressperson: this borders on interesting.
If only there were some device, --some kind of mechanism that would allow you to regulate chain tension as well as achieve different gear ratios without flipping your wheel around or prime-factoring your chainring. Or maybe some other sort of invention that allowed you to brake without wearing out your tire.
Maybe science can come up with something. Science has done good things in the past, haven't they?
Yes. Yes, they have.