Talk:Prime number theorem
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Not sure how to change that myself but the mathematical notation here is wrong:
It should not be the approx symbol (2 waves) but a symbol with 1 wave.
Strictly speaking the approy symbol is wrong, since Pi(x) is _not_ approximated
x/ln(x), but the only the limes of Pi(x)*ln(x)/x is 1, which is a different statement.
see also :
http://mathworld.wolfram.com/PrimeNumberTheorem.html
Could someone put a proof of the Prime Number Theorem here?
Paul Erdos, the legendary genuius, was the first to provide an 'elementary' proof of the prime number theorem. Should this be added?
- I don't think so. Any non-elementary proof requires considerable background and machinery from complex analysis, and the proof runs several pages. The "elementary" proof is even more difficult to follow, requires lots of preliminary estimates and results, and the proof is several pages long.
"The constant involved in the O-notation is unknown." Which constant?
- I assume this talks about the inherent constant factor that comes with O-notation. The line about Erdös (not Erdos!) should probably be added, but without the "the legendary genius" part. -- Schnee 12:22, 5 Sep 2003 (UTC)
I'd like to see added: methods for calculating pi(x), other than brute force. Bubba73 05:25, 18 Jun 2005 (UTC)
"The Selberg-Erdős work effectively put paid to the whole concept" - is "paid" a wrong word? Bubba73 05:28, 18 Jun 2005 (UTC)
Correct TeX
Do not write log\ x. That looks like this:
- <math>log\ x.<math>
Instead write \log x. That looks like this:
- <math>\log x.\,<math>
Use of backslashes in \log, \exp, \sin, \cos, \max, \min, \det, \lim, \sup, \inf and a number of other math operators has at least three effects:
- log and the like don't get italicized as if they were variables;
- proper spacing is automatic. How much space is needed depends on the context, but all of the standard conventions in this regard are built in to the TeX software;
- in some cases, e.g., \lim, \max, etc., the supscript will appear directly below the operator, rather than below and to the right, thus:
- <math>\max_{x>0} f(x).\,<math>
- <math>\lim_{x\to 0} f(x).\,<math>
Michael Hardy 23:02, 21 Jun 2005 (UTC)
- Thanks, I'm the one that used log\. (I started with TeX less than a week ago.) Bubba73 23:51, 21 Jun 2005 (UTC)