Re: Pi and the distribution of prime numbers

From: Johann Wiesenbauer (j.wiesenbauer_at_tuwien.ac.at)
Date: 02/10/05 

Date: Thu, 10 Feb 2005 13:00:49 +0000 (UTC)

On 09 Feb 2005, =?ISO-8859-1?Q?Jos=E9_Carlos_Santos?= wrote:
>Hi all,
>
>At the MathWorld page dedicated to pi, located at
>
>http://mathworld.wolfram.com/Pi.html
>
>it is claimed that pi "crops up in all sorts of unexpected places in
>mathematics [...]. For example, it occurs in [...] the distribution of
>primes". Does anyone know what's the connection? Or is it a confusion
>between the number pi and the prime counting function (usually denoted
>by pi)?
>
>Best regards,
>
>Jose Carlos Santos

In my opinion the most obvious connection between pi and the
distribution of primes is the following: The density of squarefree
numbers, that is of natural numbers not divisible by the square of a
prime, is 6/pi^2.

Johann

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