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Primes in short intervals

Hugh L. Montgomery·K. Soundararajan
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Abstract

Contrary to what would be predicted on the basis of Cramér's model concerning the distribution of prime numbers, we develop evidence that the distribution of $ψ(x+H)- ψ(x)$, for $0\le x\le N$, is approximately normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^δ\le H \le N^{1-δ}$.

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Hugh L. Montgomery, K. Soundararajan. 2004-09-15. Primes in short intervals. https://doi.org/10.1007/s00220-004-1222-4

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