Re: Probability(X is Prime)

From: david cornwell (davecornwell_at_comcast.net)
Date: 09/08/04 

Date: 7 Sep 2004 19:01:48 -0700

anonymous@mathforum.org (Bob Silverman) wrote in message news:<200409071320.i87DKkv13039@proapp.mathforum.org>...
> On 06 Sep 2004, david cornwell wrote:
> >pubkeybreaker@aol.comstuff (Bob Silverman) wrote in message news:<20040901213326.18867.00000009@mb-m01.aol.com>...
>
> <snip>
 
>
> Who is "we"?

Looks like "we" are the people writing to this thread.
 
<snip>
 
> You need to define a pdf before you can begin talking about
> probability. One such is the following:
>
> Let S = {x | (1-eps)X < x < (1+eps) X} x in Z+ for some X.
> and (say) 1/2 < eps < 1
>
> Thus, S is the set of all integers x, near X.
>
> If we select x uniformly at random from the set S, then the
> probability that x is prime is approximately 1/log(X).
>
> You can['t] take x uniformly from all of Z+; no such density function
> exists. You have to take some bounded subset of Z+.

So using your example as a good starting point for further discussion, what
values of eps and X make the statement not approximate but exact?

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