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 how the Zeta Function relates to prime numbers in the above bit of mathematics. I like it anyway.
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.