Absolutely fascinating comment regarding gears and coprimes. This is the first time I have heard of either.
My mind goes somewhere completely unrelated to the comment though: cicadas!
I believe it is a mystery why some species of cicada have have a 17-year life-cycle. Theories have included avoiding predation etc.
However, I wonder if the 17-year cycle (prime) avoids "even wear patterns" somehow in their DNA??