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I have a question concerning Bertrand's postulate in "Proofs from the BOOK", on page 8:

$\prod_{p \leq {2m+1}} p=\left(\prod_{p \leq m+1} p \right)\left( \prod_{{m+1}

Why did the author split the product up in the way he did it and not in another way? Are there any reasons?

Any help would be appreciated.

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    So the thing to do now is to post the answer you have found, and then accept it, so we can all get on with other things. It may sound like a strange idea, but it's actually the way the site works.2011-11-22

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Sorry for answering my own question, but I found the reason:

For the first product holds

$\prod_{p \leq m+1} p \leq 4^m$

and for the 2nd

$\prod_{{m+1}

especially $\binom{2m+1}{m}=\frac{2m+1!}{m!m+1!}$ and thus, we get for the 2nd intervall primes which divides not the denominator but the numerator.

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    It's possible within 23h2011-11-23