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Primes in short intervals
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Primes in short intervals
classification
math.NT
keywords
deltadistributionapproximatelybasisconcerningcontrarycramdevelop
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Contrary to what would be predicted on the basis of Cram\'er's model concerning the distribution of prime numbers, we develop evidence that the distribution of $\psi(x+H)- \psi(x)$, for $0\le x\le N$, is approximately normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^\delta \le H \le N^{1-\delta}$.
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