Primes get all the attention, but composite numbers are individually more interesting, having varied and unique factorizations. The main way primes become individually interesting is through the factorization of the composite p-1, which induces the structure of its multiplicative group.
What are some ways to bring out the beauty of the composites?
Color them so that smooth numbers are easy to spot: color by the largest prime factor. On the other end of the spectrum, primes and semiprimes could look practically alike.
Color by the magnitude of the smallest prime factor. There will be stripes caused by multiples of small primes: maybe do some processing to eliminate some of the stripes to see more subtle structure?
Investigate twin smooths: smooth numbers which are unusually near each other, inspired by twin primes.
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