- Hi,

If by Nth index you mean pi(x) then:

pi(123571113171923) = 3933667972530

pi(231917131175321) = 7237459689186

pi(1235711131175321) = 36647548937934

pi(1357911131197531) = 40159216312772

The next one is too big for my implementation and I do not think anyone knows pi(R23) for sure. I could provide good approximations.

- David

--- In primenumbers@yahoogroups.com, Ali Adams <alipoland@...> wrote:

>

> Peace to all,

>

> Can someone please tell me what is the best way to find the Nth index of the following not so large prime numbers?

>

> 12345678910987654321 (from 1 to 10 and back)

>

> 1357911131197531 (odds from 1 to 13 and back)

>

> 1235711131175321 (primes from 1 to 13 and back)

>

> 123571113171923 (primes from 1 to 23)

>

> 231917131175321 (primes from 23 to 1)

>

> and

>

> 11111111111111111111111 (23 ones)

>

> Thank you all.

>

> Ali Adams

> God > infinity

> www.heliwave.com

>

>

>

>

>

>

>

> [Non-text portions of this message have been removed]

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

David Baugh <PbtoAu@...> wrote:

> pi(1357911131197531) = 40159216312772

How did you compute pi(x) with x > 10^15, please, David?

> The next one is too big for my implementation

Andrew Booker's programme hosted at

http://primes.utm.edu/nthprime/

is restricted to pi(x) with x < 3*10^13.

For those with dollars to burn, Mma seems

able to compute pi(x) with x < 8*10^13:

http://mathworld.wolfram.com/PrimeCountingFunction.html

It seems that you have an implementation that

comfortably copes with x > 10^15.

Might you consider making your code available to

Chris Caldwell, for on-line use at the Prime Pages,

as Andrew generously did with his? If the data tables

are too big or the CPUtime too onerous for such on-line use,

might you kindly provide a source that others may compile?

Best regards

David Broadhurst - David Broadhurst wrote:
> David Baugh <PbtoAu@...> wrote:

I don't know what David Baugh uses but there is something better.

>

>> pi(1357911131197531) = 40159216312772

>> The next one is too big for my implementation

>

> How did you compute pi(x) with x > 10^15, please, David?

At http://mersenneforum.org/showthread.php?t=13210 I wrote:

"Two years ago I searched for a good pi(x) program, found an old mention

of Christian Bau and dug up a link to http://www.cbau.freeserve.co.uk

The link was and still is dead but the Wayback Machine has archived

versions up to 2005 at

http://web.archive.org/web/*/http://www.cbau.freeserve.co.uk.

There is C++ source by Christian Bau for the Extended Meissel-Lehmer

algorithm. It works to 2^64 and my test runs agree with published counts

by Tomás Oliveira e Silva. I have used the program for a few projects

such as http://primes.utm.edu/curios/includes/puzzio.php. The archive has

Version 0.92, 25/Sep/2003. The site speaks of unfinished work in

progress and mentions future improved versions but I have not found that."

It takes 1 minute for the program to compute pi(1357911131197531) on

one core of a 2.4 GHz Core 2 Duo. The value agrees with David Baugh.

--

Jens Kruse Andersen - --- In primenumbers@yahoogroups.com,

"Jens Kruse Andersen" <jens.k.a@...> wrote:

> Two years ago I searched for a good pi(x) program,

Thanks, Jens!

> found an old mention of Christian Bau and dug up a link to

> http://www.cbau.freeserve.co.uk [broken URL]

web.archive.org/web/20040125140056/http://www.cbau.freeserve.co.uk/

seems to be an appropriate archived URL. "PrimeCount.cp" says:

> This code is unfinished work in progress. For this reason,

which seems to permit personal use.

> you may download this code and use it on the computer that

> you used for downloading, but any further distribution is

> strictly prohibited.

David - Looks like Bau's code goes twice as high as Baugh's code and I don't have source code. The code the community needs is that developed by Tomás Oliveira e Silva. His can go to at least 10^23. I have asked, but I guess not nicely enough.

- David

--- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:

>

>

>

> --- In primenumbers@yahoogroups.com,

> David Baugh <PbtoAu@> wrote:

>

> > pi(1357911131197531) = 40159216312772

> > The next one is too big for my implementation

>

> How did you compute pi(x) with x > 10^15, please, David?

>

> Andrew Booker's programme hosted at

> http://primes.utm.edu/nthprime/

> is restricted to pi(x) with x < 3*10^13.

>

> For those with dollars to burn, Mma seems

> able to compute pi(x) with x < 8*10^13:

> http://mathworld.wolfram.com/PrimeCountingFunction.html

>

> It seems that you have an implementation that

> comfortably copes with x > 10^15.

>

> Might you consider making your code available to

> Chris Caldwell, for on-line use at the Prime Pages,

> as Andrew generously did with his? If the data tables

> are too big or the CPUtime too onerous for such on-line use,

> might you kindly provide a source that others may compile?

>

> Best regards

>

> David Broadhurst

>