What's in a number? Well, prime roots, for one thing. I'm sure there are many other "significant" ways to understand a given integer, but prime roots seem like they get at some kind of fundamental essence. Take 12, for instance. 2, 2 and 3.
Just for fun, let's pretend that quarks represent prime numbers. If up quarks were "2", and down quarks were "3", that would give you a proton, so a proton would be 12. A neutron would be 18, since it has 2 down quarks and 1 up quark (2, 3 and 3). We might have to create some imaginary quarks to go much further, but this obliquely conveys my excitement about prime roots being "fundamental building blocks of numbers".
Not seeing a particularly simple prime root calculator, I created this:
prime root finder