I am looking to see whether historic mathematicians did any work to explain the slightly unexpected distribution of prime gaps?

I would have expected Gauss, who studied lists of primes and proposed a form for their average density $1/\log(n)$, to have considered this question too?

The following chart plots the log of prime gap counts for each gap in the number range 1 to 500 million. It is unusual to see such a linear and tightly bounded shape.

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I believe, but am not certain, that no results have been proven to explain the shape of this distribution.

  • $\begingroup$ Gauss did not look into prime gaps, but I am guessing that this shape is reproduced by Cramer's random model. There are also oscillations in the graph related to divisibility by 6 that can be accounted for by known corrections to it. $\endgroup$
    – Conifold
    Commented Apr 16, 2021 at 0:39
  • $\begingroup$ Some google-fu leads me to this paper, which could be a starting point for a more extensive search. $\endgroup$
    – Danu
    Commented Apr 16, 2021 at 12:20


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