0
$\begingroup$

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.

enter image description here

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

$\endgroup$
2
  • $\begingroup$ 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

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.