\(f(x)\) denotes the number of *different* prime factors of the integer \(x\), excluding \(1\) and \(x\) itself. For example, since \(12=2\times2\times3\), then \(f(12)=2\).

- Calculate \(f(121)\).
- Calculate \(f(17)\).
- Write down the smallest \(x\) for which \(f(x)=4\).