Sampling and Experiments · Superchallenge problem

A factory numbers its machines $1, 2, \ldots, N$. An inspector sees a simple random sample of 4 distinct serial numbers and records the largest one, $M$. For which constant $c$ is $cM - 1$ an unbiased estimator of $N$ (that is, $E[cM - 1] = N$ for every $N \ge 4$)?