In this research, we examine a special property of some prime numbers that goes beyond separating primes from odd composites. Rather, this property serves to divide the set of primes into two groups: those having it and those lacking it. Incredibly, these two groups portray an almost equal distribution of primes amongst them. This phenomenon is explored in order to reveal some aspects concerning the basic characteristics and structure of prime numbers. We also provide further insight on what this trait implies within prime number theory through rigorous analysis as well as mathematical inspection which shines a new light on the enigmatic properties of these fundamental mathematical entities.