- Jarek,

I might be interested in helping to set up a distributed system. Since each

segment is independent, this shouldn't take anything fancy. I am a professional

web programmer and could manage this as a web project in a database. That

way people could easily request segments and get them assigned.

Is your program just source at this point? Or do you have a stand alone exe?

Someone else might be able to put together an windows version.

I have also looked at PrimeGrid and this is probably the best way to distribute

the project. Does anyone here have experience on that system?

Paul

----- Original Message -----

From: jarek372000

To: primenumbers@yahoogroups.com

Sent: Saturday, May 17, 2008 5:45 AM

Subject: [PrimeNumbers] Re: AP25

I am not sure what was the exact CPU power used, as Raanan was

distributing the program among his computers, and also the number and

kind of computers he had access to, varied. However, I understand you

are asking what order of magnitude of CPU takes to find such a result.

I think we weren't either particularly lucky or unlucky. Data gathered

during the search indicates that it was about time to expect the first

AP25.

The search was in a natural way divided into many independent

segments, each taking about 3 minutes on Athlon 64, it would take some

10 times more on a 32-bit computer, otherwise it depends on the

particular processor. Probably no RAM is used, processor cache should

be enough. I think Raanan went through less than 10,000,000 such

segments before finding the AP25 - this would be somewhat lower if we

targeted AP25 from the start since we would have scheduled the search

differently.

To hunt AP26, the program could be speed up by a factor of 2, at the

cost of missing about one third of AP25's on the way of current

search, but with no loss of AP26's. I think that one would have to go

through something like 500,000,000 segments without finding AP26, to

be eligible to complain on bad luck.

So we are talkig about at least 1000 CPU years of 64-bit computers to

honestly expect an AP26.

Now, I am not a professional programmer. I have written a C-code which

can be run on a single computer, and in consequence it can be run on a

local network with a proper script. I have no ability to make a

distibuted project on the network. If someone is interested in running

a wide distributed search, I can provide the code. Program segments

are numbered, so in principle you can distribute the search ranges by

sending out to everyone a New Year postcard once a year with the

assigned range for the next year. Or with a few hundred million of

computers you can find AP26 in a few minutes (provided you can

distribute the numbers of segments).

Jarek

--- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:

>

> --- On Sat, 5/17/08, jarek372000 <Jaroslaw.Wroblewski@...> wrote:

> > This morning the first known AP25 has been discovered:

> >

> > 6171054912832631 + 366384*23#*n, for n=0 to 24

> > (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008)

> >

> > My contribution was the search program, while Raanan

> > provided the computer power.

>

> Wow! A marvelous find. I think a lot of people here have been

crossing their fingers for you over the last few months as the AP24s

have been coming in, I certainly have.

>

> What kind of CPU power was behind the task? Does your program

sensibly distribute? I'd certainly be willing to stick a CPU or two on

a distributed project that was pushing for an AP26. However, my fear

is that the bandwidth/comms issues might be cause Amdahl's law to

frown at such a task.

>

> Phil

>

[Non-text portions of this message have been removed] - Jarek wrote:
> This morning the first known AP25 has been discovered:

Huge congratulations!

>

> 6171054912832631 + 366384*23#*n, for n=0 to 24

> (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008)

>

> My contribution was the search program, while Raanan provided the

> computer power.

This is a very impressive and well deserved feat.

http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

As the only known AP25 it gets 5 records: Longest known AP, largest

known AP25, and smallest known difference, start and end for an AP25.

Getting 5 records for one AP may sound like a lot but it's much more

than 5 times as hard as most of the other records.

--

Jens Kruse Andersen - Jens Kruse Andersen wrote:
> Huge congratulations!

I agree! Decided to change my 2006 banner notes about the last

> This is a very impressive and well deserved feat.

> http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

Mersenne to this AP on my "main" page primes.utm.edu/

and primes.utm.edu/largest.html

> Getting 5 records for one AP may sound like a lot but it's

We know they exist with arbitrary length, but 25 seems a long

> much more than 5 times as hard as most of the other records.

way from infinity doesn't it?

CC - Chris Caldwell wrote:

> I agree! Decided to change my 2006 banner notes about the last

Nice. I see it's already in Prime Curios!:

> Mersenne to this AP on my "main" page primes.utm.edu/

> and primes.utm.edu/largest.html

http://primes.utm.edu/curios/page.php/6171054912832631.html

This can also be updated:

http://primes.utm.edu/glossary/page.php?sort=ArithmeticSequence

> We know they exist with arbitrary length, but 25 seems a long

Yes it does. I made a similar "but" when Jarek's earlier record was

> way from infinity doesn't it?

mentioned on Wikipedia's main page in 2007 with the text:

"Did you know...

...that existence of arbitrarily many primes in arithmetic progression was

proven in 2004, but it took 75 computers to find an example with 24 primes?"

It's archived at

http://en.wikipedia.org/w/index.php?title=Template:Did_you_know&oldid=138995374

(People are not supposed to know the "Did you know" facts)

I have updated http://en.wikipedia.org/wiki/Primes_in_arithmetic_progression

--

Jens Kruse Andersen