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Thursday, November 17, 2016

**Abstract:** Beatty sequences are generalized arithmetic progressions which have been studied intensively in recent years. Thanks to the work of Vinogradov, it is known that every Beatty sequence S contains "appropriately many" prime numbers. For a given pair of Beatty sequences S and T, it is natural to wonder whether there are "appropriately many" primes in S for which the next larger prime lies in T. In this talk, I will show that this is indeed the case if one assumes a certain strong form of the Hardy-Littlewood conjectures. This is recent joint work with Victor Guo.