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> It ain't as pretty as just between straight integer multiples, but the fact that it exists in some shape at all is cool!

Actually: the form that Larsen proved is stronger than "for sufficiently large X, there is at least one Carmichael number between X and 2X".

So with the more specific proof, he also proved the simpler statement that's easier to express.

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What is the stronger version?

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

Thank you!

Haha very good!

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