Think of it more like fundamental research. Maybe nobody could make immediate productive use of the discovery of (for example) radioactivity in the late 1800s,

Think of it more like fundamental research. Maybe nobody could make immediate productive use of the discovery of (for example) radioactivity in the late 1800s, but it has a wide variety of uses today from energy production to medical imaging. It's unlikely that proof of the twin prime conjecture would prove that fundamental, but the results are hard to predict in advance.