Proof Writing & Problem Solving · Superchallenge problem

The claim "if $p$ is prime, then $2^p - 1$ is prime" holds for $p = 2, 3, 5, 7$ but fails for $p = 11$, since $2^{11} - 1 = 2047 = 23 \cdot 89$. It fails again for $p = 23$. What is the smallest prime factor of $2^{23} - 1$?