The Riemann Hypothesis is one of the most famous open problems in mathematics, and if proven it would have amazing consequences for our understanding of prime numbers.

It turns out many of these applications to primes would still be true even if the Riemann Hypothesis was false, provided counterexamples to the Riemann Hypothesis are suitably ‘rare’. I’ll give an accessible talk about this and some recent work showing how ‘patterns’ of zeros are related to our understanding of primes.