Big advance on simple-sounding math problem was a century in the making

> another asks whether there are infinitely many pairs of primes that differ by only 2, such as 11 and 13

Is it that many questions were successfully dis/proved and so were left with some that seem arbitrary? Or is there something special about the particular questions mathematicians focus on that a layperson has no hope of appreciating?

My best guess is questions like the one above may not have any immediate utility, but could at any time (for hundreds of years) become vital to solving some important problem that generates huge value through its applications.