There is a fun meme wandering about that proports to explain why the Cicadias pop out on cycles that are long prime numbers of years.
Are there other things in life that intentionally use prime numbers to avoid synchronization? Could this be the reason that weeks are seven days, and months strive to be 31? Are there traffic light synchronization or land development patterns that avoid synchronization? Do some of the peer to peer systems use prime numbers to reduce chance congestion? Could prime numbers play a role in regulatory systems to temper the natural tendencies toward market concentration?