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I need some advice: I'm dealing with the proof of Bertrand's postulate Proofs from THE BOOK. I understood the proof completly but as I tried to make a drawing of the intersection of the lower und upper boundary (which should be refering to the book at n=4000) I got some strange results.

My result for the intersection is round about n=5000. If someone has an explanation for it, it would be great.

Thanks a lot in advance.

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Clearly, from $2^{2n}<2^{20(2n)^{2/3}}$ we may conclude $2n<20(2n)^{2/3}$, then $(2n)^{1/3}<20$ and finally $n<\frac{20^3}2=4000$. I have no idea what you did instead.

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    Hm interesting, that is exactly the wrong implication I made. But can someone explain, why the implication n is wrong?2012-11-08