Re: [PrimeNumbers] Re: AP25
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?
----- Original Message -----
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
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
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).
--- In email@example.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.
[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/
> Getting 5 records for one AP may sound like a lot but it'sWe 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?
- Chris Caldwell wrote:
> I agree! Decided to change my 2006 banner notes about the lastNice. 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
This can also be updated:
> We know they exist with arbitrary length, but 25 seems a longYes 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
(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