I don't know if it is possible, but could you explain Dirichlet's theorem on arithmetic progressions and Green–Tao theorem to someone with, uhm, good knowledge of *high-school* math, but not much beyond that?

In general I wonder how can *anything* be proved about prime numbers (other than the fact that they are infinitely many), because they seem to appear quite randomly.

EDIT: I will accept if the inferential distance is simply too large. I am just hoping that maybe it isn't.

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