Bertrand's postulate is that there is at least one prime between x and 2x for x>=1

Daniel Larsen's result here is that there are e^((log x)/((log log x)^(2+d))) Carmichael numbers between x and (x + x/((log x)^(1/(2+d)))) for x>=X (depends on d)

e^((log x)/((log log x)^(2+d))) is >= 1 for all x >= 1.

(x + x/((log x)^(1/(2+d)))) <= 2x

Stronger by being tighter than the (x,2x) bound and being more specific about the >= 1 number of Carmichael numbers