2020/09/10 by Granville, Andrew, Lumley, Allysa
#11B83 #11N05 #11N35 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2009.05000
We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length y around x, where y≪ (log x)2. In particular we conjecture that the maximum grows surprisingly slowly as y ranges from log x to (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.