# Fractal Sets and Arithmetic Progressions

If a set of positive integers contains no arithmetic progressions, how large can it be? In this post, we study this question in the context of harmonic sums.

Just how good are polynomials at producing primes? Do there exist polynomials that produce primes for arbitrarily many consecutive inputs?

In this post, I’ll give a brief overview of what we expect to be able to prove, and show how interpolating polynomials can produce record-breaking prime-generators. (And then break a record, because why not?)