Is that there is some insight into the nature of primes that comes from considering the classes of numbers that share the same set of prime factors. For example

2x3x5 = 30, 4x3x5 = 60, 2x9x5 = 90, 2x3x25 = 150, 4x3x25=300 …

all of these have the same set of prime divisors {2,3,5}

in fact, each of these classes of numbers is generated by a unique square-free-number.