I've checked the factorization of $2^N - 1$ up through N = 120 for the largest prime factor, and it looks like the largest value of N where $2^N-1$ has a largest prime factor under 2500 is N = 60 (largest prime factor = 1321). As N gets larger, the largest prime factors get larger, even for the "abundant" numbers like 96, 108, and 120.

Is there a way to prove that no value of N > 60 exists such that the largest prime factor of $2^N - 1$ is less than 2500?