6 ms·
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 https://en.wikiped
by qmalzp 9y ago
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 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 9y ago> 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.