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I'm looking at Theorem 3 of this paper, which is

If $\:x\geq \exp(\exp(45))\:$ and $\;\;h\:\geq\:3\cdot x^{\frac23}\;\;$ then $$\pi(x+h)-\pi(x) \; \geq \; h\cdot \left(1-\left(3192.34\cdot \exp\left(\left(-\frac1{283.79}\right)\cdot \left(\left(\frac{\log(x)}{\log(\log(x))}\right)^{\frac13}\right)\right)\right)\right)$$



The term starting with 3192.34 goes to zero as $x$ goes to infinity, which results in
$\pi(x+h)-\pi(x) \: \approx \: h \: = \: (x+h)-x \: \not\approx \frac{(x+h)-x)}{\log(x)} \;\;$,
contradicting the prime number theorem.


What am I missing here?

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closed as off-topic by Felipe Voloch, Andres Caicedo, Andy Putman, John Pardon, Alain Valette Aug 18 '13 at 6:20

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – Felipe Voloch, Andres Caicedo, Andy Putman, John Pardon, Alain Valette
If this question can be reworded to fit the rules in the help center, please edit the question.

3  
It's a typo. Should have been $h/\log x$ times blah. Look at the proof (which is three lines long). –  Felipe Voloch Aug 18 '13 at 2:40
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