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Can anyone prove or disprove the following statement?

$$ \lim_{n \to \infty} \frac{p_{n+1} - p_{n}}{\sqrt{p_n}} = 0.$$

  • 14
    I'm guessing $p_n$ is meant to the be $n$th prime? Ideally, one should not be forced to *guess*, though, and the government doesn't like it when I read minds without a warrant.2012-07-23
  • 1
    Partial results are available at http://en.wikipedia.org/wiki/Prime_gap#Further_results.2012-07-23

3 Answers 3