Accidents of small $n$ In studying mathematics, I sometimes come across examples of general facts that hold for all $n$ greater than some small number. One that comes to mind is the Abel–Ruffini theorem, which states that there is no general algebraic solution for polynomials of degree $n$ except when $n \leq 4$.
It seems that there are many interesting examples of these special accidents of structure that occur when the objects in question are "small enough", and I'd be interested in seeing more of them.

The ring of integers of $\mathbf{Q}[\sqrt d]$ is a principal ideal domain for $1 \leq d < 10$, but not for $d=10$.
