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Thursday, October 5, 2017

**Abstract:** In recent decades there have been significant advances made in finding primes in "thin" sequences. One such advance was the work of Friedlander and Iwaniec, in which they proved there are infinitely many primes that can be represented as the sum of a square and a biquadrate. A more recent advance is due to Maynard, who showed the existence of infinitely many primes in the thin sequence of integers missing a fixed digit in their decimal expansion. In this talk I discuss a marriage of some of the ideas of Friedlander-Iwaniec and Maynard which allows one to find primes in other interesting thin sequences.