Bounded Gaps Between Primes learning seminar

“Estimates for Improving Zhang’s Bounded Gaps of Primes”

In 2013 Yitang Zhang proved that there are an infinitely many pairs of primes such that the two 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 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 obtained this number by strenghening Zhang’s estimates for Type I, Type II, and Type III. We examine these estimaes and show how these estimates imply Zhang’s theorem.