The next talk in the learning seminar for bounded gaps between primes will be this upcoming **Wednesday, January 29th **in room **MC 4062, **at **4:00 PM. **The speaker this week is John C. Saunders, a PHD student in the Pure Mathematics Department. The title and abstract is below.

**Estimates for Improving Zhang’s Bounded Gaps of Primes**

In 2013 Yitang Zhang that there are infinitely many pairs of primes such that the primes in each pair differ by no more than 70,000,000. One of the techniques he used to prove this is to reduce the problem down to three types of estimates, which he named Type I, Type II, and Type III. A refinement of this his argument was given by the Polymath Project whose goal is to reduce the gap of 70,000,000 and did so to 4680. They did so by strengthening Zhang’s estimates for Type I, Type II, and Type III. We examine these estimates and show how these estimates imply Zhang’s theorem.

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