Schatunowsky's Theorem

Theorem
Let $n \in \Z_{>0}$ be a strictly positive integer.

Let $\map w n$ denote the number of primes strictly less than $n$ which are not divisors of $n$.

Let $\map \phi n$ denote the Euler $\phi$ function of $n$.

Then $30$ is the largest integer $n$ such that:
 * $\map w n = \map \phi n - 1$

Also see

 * Integers such that all Coprime and Less are Prime