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Short intervals with a given number of primes | | Tristan Freiberg
; | | Date: |
1 Aug 2015 | | Abstract: | A well-known conjecture asserts that, for any given positive real number
$lambda$ and nonnegative integer $m$, the proportion of positive integers $n
le x$ for which the interval $(n,n + lambdalog n]$ contains exactly $m$
primes is asymptotically equal to $lambda^me^{-lambda}/m!$ as $x$ tends to
infinity. We show that the number of such $n$ is at least $x^{1 - o(1)}$. | | Source: | arXiv, 1508.0143 | | Services: | Forum | Review | PDF | Favorites | |
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