Bounded prime gaps in short intervals

2013/06/03 by Andersson, Johan
#11N #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1306.0511

Abstract

We generalise Zhang's and Pintz recent results on bounded prime gaps to give a lower bound for the the number of prime pairs bounded by 6*10⁷ in the short interval [x,x+x (log x)^-A]. Our result follows only by analysing Zhang's proof of Theorem 1, but we also explain how a sharper variant of Zhang's Theorem 2 would imply the same result for shorter intervals.

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