- Hi all,

Newbie with a newbie question here. Other than Riemann Hypothesis is no other way to calculate 'exact' P(x)?

If there was such a method then somebody could do the opposite of Riemann and work from the solution by adding waves to get to x/Li(x)?

In other words prove RH by downgrading the exact result to meet the PNT estimate of x/Li(x)?

Thanks

TechnoBuddhist - --- In primenumbers@yahoogroups.com,

"techno.buddhist" <yahoo@...> wrote:

> Other than Riemann Hypothesis is no other way

This method

> to calculate 'exact' P(x)?

http://www.dtc.umn.edu/~odlyzko/doc/arch/meissel.lehmer.pdf

require O(x^(2/3)) operations and O(x^(1/3)) bits of storage.

> If there was such a method then somebody could do the

http://www.dtc.umn.edu/~odlyzko/doc/zeta.html

> opposite of Riemann and work from the solution by adding

> waves to get to x/Li(x)?

contains relevant papers

David - One of the problems, I think, that you might bump into is that many of the interesting combinatorial prime counting algorithms out there (like the method djbroadhurst linked to) don't seem to have any obvious connection to the logarithmic integral, so it's hard to know where you would add the error terms back in.

In addition to dj's links, if you're really interested in playing around with this approach, one set of ideas you might take a look at is this:

http://www.icecreambreakfast.com/primecount/logintegral.html

(warning: I just wrote this up last week, so consider this un-peer-reviewed, suspect, and possibly self-aggrandizing) It actually has some reasonable raw material for an attempt at what you're talking about, I think.

Nathan McKenzie

--- In primenumbers@yahoogroups.com, "techno.buddhist" <yahoo@...> wrote:

>

> Hi all,

>

> Newbie with a newbie question here. Other than Riemann Hypothesis is no other way to calculate 'exact' P(x)?

>

> If there was such a method then somebody could do the opposite of Riemann and work from the solution by adding waves to get to x/Li(x)?

>

> In other words prove RH by downgrading the exact result to meet the PNT estimate of x/Li(x)?

>

> Thanks

>

> TechnoBuddhist

> - Hello, I was wondering if it is possible to get a list of all multiples < Cte

under the form: a / a^2 / b / b*a / b^2 /.... < Cte very easily, or do this kind of computations gets messy quickly?

________________________________

From: djbroadhurst <d.broadhurst@...>

To: primenumbers@yahoogroups.com

Sent: Sunday, September 11, 2011 6:30:11 AM

Subject: [PrimeNumbers] Re: P(x) question?

--- In primenumbers@yahoogroups.com,

"techno.buddhist" <yahoo@...> wrote:

> Other than Riemann Hypothesis is no other way

This method

> to calculate 'exact' P(x)?

http://www.dtc.umn.edu/~odlyzko/doc/arch/meissel.lehmer.pdf

require O(x^(2/3)) operations and O(x^(1/3)) bits of storage.

> If there was such a method then somebody could do the

http://www.dtc.umn.edu/~odlyzko/doc/zeta.html

> opposite of Riemann and work from the solution by adding

> waves to get to x/Li(x)?

contains relevant papers

David

[Non-text portions of this message have been removed] - I looked at your work, I got mesmerised by the eye candy for a while(I build the odd website now and again and the flash apps really caught my attention). If the flash apps are your work, well done, very nice!

Took me a while before I got it(my head obviously wasn't in the zone) but the basic gist is what interested me anyway. Using integration to approximate is an interesting approach. I'll see if it can be used in my work.

Thanks, very informative!

TechnoBuddhist

--- In primenumbers@yahoogroups.com, "kenzi_x" <nathan@...> wrote:

>

> One of the problems, I think, that you might bump into is that many of the interesting combinatorial prime counting algorithms out there (like the method djbroadhurst linked to) don't seem to have any obvious connection to the logarithmic integral, so it's hard to know where you would add the error terms back in.

>

> In addition to dj's links, if you're really interested in playing around with this approach, one set of ideas you might take a look at is this:

>

> http://www.icecreambreakfast.com/primecount/logintegral.html

>

> (warning: I just wrote this up last week, so consider this un-peer-reviewed, suspect, and possibly self-aggrandizing) It actually has some reasonable raw material for an attempt at what you're talking about, I think.

>

> Nathan McKenzie

>

> --- In primenumbers@yahoogroups.com, "techno.buddhist" <yahoo@> wrote:

> >

> > Hi all,

> >

> > Newbie with a newbie question here. Other than Riemann Hypothesis is no other way to calculate 'exact' P(x)?

> >

> > If there was such a method then somebody could do the opposite of Riemann and work from the solution by adding waves to get to x/Li(x)?

> >

> > In other words prove RH by downgrading the exact result to meet the PNT estimate of x/Li(x)?

> >

> > Thanks

> >

> > TechnoBuddhist

> >

>