Hi, Prof. CC.
maximal gap either above or below a number x:
without proof, probably already known...
just a my idea of a postulate, axiom, etc. concerning gaps
Ji(x) = Eta [sqrt(x)/(ln(x))^k] for k = 0 to floor(sqrt(lnx)))
Best examples in the 'small' as you stated.
I'm aware of the law of small numbers.
x = 11; Ji(11) = sqrt(11)/1 + sqrt(11)/ln(11) = 4.699+/-;
x = 127; Ji(127) = sqrt(127)/1 + sqrt(127)/ln(127) + sqrt(127)/(ln(127))
^2 = 14.07+/-;etc.
Please provide me with a relatively small counter-example, < x = 10^316
Best regards, Bill
Anyway, I do think that your website is commendable.
Remember,... I'm not saying qed... just exhibiting a formula
For now, ...Je fermerai ma bouche.