Re: On using Prime Counting Function in proofs


quasi wrote:
> On Wed, 05 Oct 2005 14:29:25 +1000, Gerry Myerson
> <gerry@xxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
>
> >In article <1128483417.924371.44960@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> > "Joubin Houshyar" <Sun_of_27@xxxxxxxxx> wrote:
> >
> >> Gerry Myerson wrote:
> >> > In article <1128209425.300282.86040@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> >> > "Joubin Houshyar" <Sun_of_27@xxxxxxxxx> wrote:
> >> >
> >> > > If the proof is trying to establish a minimum bound for a certain
> >> > > function X(n), and 'undercounting' Pi(n) is acceptable (in the proof*)
> >> > > is the simple "pi(n) > n/ln(n)" acceptable as a correct approximation
> >> > > for pi(n)?
> >> >
> >> > Do you know for a fact that pi(n) > n / (log n) for all n?
> >>
> >>
> >> http://mathworld.wolfram.com/PrimeCountingFunction.html
> >>
> >> "[...] for n>=17 (Rosser and Schoenfeld 1962) [...]"
> >
> >Good - then what's the problem? If pi(n) > n / (log n) for n > 17
> >then what's to stop you from using n / (log n) as a lower bound
> >for pi(n)? What could possibly go wrong?
>
> He's asking permission.

Actually I wasn't asking your "permission" quasi. I vaguely remembered
reading that a given asymptotic form of pi(n) had been recently shown
to cross for very large n's. I wasn't sure if it was the above and
needed to confirm that it was not.

.

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