Brian Beesley wrote:
> On Sunday 01 October 2006 18:28, Soo Reams wrote:
>
>>Brian Beesley wrote:
>>
>>>Doesn't this depend on the (AFAIK unproved) Riemann hypothesis?
>>
>>Not certain of this, but I think Pi(x) is defined as the number of
>>primes less than or equal to x. The Riemann hypothesis is concerned with
>>a particular approximation to Pi(x), a more accurate one than Pi(x) = x
>>/ lg x.
>
>
> Isn't it _perfectly_ accurate _unless_ RH is _false_?
Absolutely not. Even if RH is true, it is not perfectly accurate.
Pi(18) = 7
18/ln(18) ~ 6.23
18/lg(18) ~ 4.3
Pi(19) = 8
19/ln(19) ~ 6.45
So it is not even "chose closest integer".
(lg x often means log base 2 of x)
Mike
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