I think that mathematically interested sixth formers, wanting to study the subject at University, should have some background knowledge. Many would have heard about the Riemann Hypothesis and a link to prime numbers; this subject is beyond the scope of this blog but school pupils, with knowledge of prime numbers and geometric progressions, can see …
Prime numbers hang like beads on a necklace (except that would be cosh …) on this quadratic.
Ancient Greek, geometric view of prime numbers.
Some prime numbers calculated by a quadratic.