Why does C++ rand() seem to generate only numbers of the same order of magnitude?

There are only 3% of numbers between 1 and 2³⁰ which are NOT between 2²⁵ and 2³⁰. So, this sounds pretty normal 🙂

Because 2²⁵ / 2³⁰ = 2^-5 = 1/32 = 0.03125 = 3.125%