Are prime numbers randomly distributed, or is there an underlying structure that can predict where they will occur?
If you can definitively answer that question, say by either proving or disproving the Riemann Hypothesis, which says that yes, there is such an underlying structure, there's a million dollar prize waiting for you.
But if you just want to explore some the patterns that can be found in how prime numbers are distributed, you might find the following 22-and-a-half minute video from 3Blue1Brown right up your alley!
As a bonus, in addition to an introduction to Dirichlet's prime number theorem, you'll also find out why the fraction 355/113 is a particularly good rational approximation for the value of pi!