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