[qmalzp]

The average gap is log(n), but the maximal gap is not well understood.

According to https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_conjecture, current results are

Unconditional: n^0.525

Conditional on RH: log(n)*sqrt(n)

Conjecturally: log(n)^2

[chx]

> It is still probably true that for every constant {\displaystyle c>2} c>2, there is a constant {\displaystyle d>0} d>0 such that there is a prime between {\displaystyle x} x and {\displaystyle x+d(\log x)^{c}} {\displaystyle x+d(\log x)^{c}}

That's quite fascinating.