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I recently read a very good inequality concerning the no of primes $\pi(x)$:

$$\pi(n)>\frac{1}{6}\frac{n}{\log n}\mathrm{\ for\ }n\ge 2$$

Are any other such elementary inequalities concerning the primes?

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closed as not a real question by KennyTM, falagar, Grigory M, BlueRaja - Danny Pflughoeft, Qiaochu Yuan Aug 10 '10 at 16:49

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

    
Could you just chop those blanks in page 2? –  KennyTM Aug 10 '10 at 9:26
    
i33.tinypic.com/s1q6jd.png –  J. M. Aug 10 '10 at 10:47
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See the discussion at mathoverflow.net/questions/26342/… –  David Speyer Aug 10 '10 at 13:16
    
@Chandru1: I've edited the question to remove the scans of the text, since you didn't give any indication of where it came from (with a citation, that kind of quoting might be okay), and to change the question to ask what you said you wanted to know in your comment on lhf's answer. If you don't agree with my edits, please feel free to re-edit the question. –  Isaac Aug 10 '10 at 16:41
    
This is a valid question –  Casebash Aug 14 '10 at 6:39

1 Answer 1

up vote 0 down vote accepted

What is your question? This is well-known stuff. It appears for instance in section 4.5 of Apostol's Introduction to Analytic Number Theory, which also contains an upper bound. You could at least say where you got yours from. (This should have been a comment, not an answer, but I don't have enough reputation for adding comments.)

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Yes it does appears in Tom Apostol's book, but what i wanted to know is whether there are any other such elementary inequalities concerning the primes. –  anonymous Aug 10 '10 at 12:42