U of Lethbridge Number Theory and Combinatorics Seminar: Allysa Lumley (Online)

We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length yy around xx, where y≪(logx)^2y≪(log⁡x)^2. In particular, we conjecture that the maximum grows surprisingly slowly as yy ranges from logxlog⁡x to (logx)2(log⁡x)^2. We will show that our conjectures are somewhat supported by available data, though not so well that there may not be room for some modification. This is joint work with Andrew Granville.