Van Der Waerden Numbers

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UBT - Chris
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Van Der Waerden Numbers

Post by UBT - Chris » Thu Mar 19, 2015 8:10 pm

All,

There is a new project up called Van Der Waerden Numbers, here is a little description:
The sequence of colors BRRBBRRB (where B is blue and R is red) does not have an evenly spaced subsequence of length 3 that are the same color. However, if you add a B to the end, you get BRRBBRRBB, which has the same color B in positions 1,5, and 9 which are evenly spaced 4 apart. If you add an R to the end, you get BRRBBRRBR, which has R at position 3, 6, and 9. In fact, with only two colors, there is no sequence of length 9 of Bs and Rs that does not have a subsequence of 3 evenly spaced of the same color. Van der Waerden's Theorem states that for any number of colors r and length k, a long enough sequence always has an evenly spaced subsequence of the same color. The smallest length guaranteed to have an evenly spaced subsequence is called the Van Der Waerden Number and is written W(k,r). For example, W(3,2)=9. This project is to find better lower bounds for Van Der Waerden Numbers by finding sequences like BRRBBRRB.

Here is how the program works. Take a prime number n (shown in parentheses on the table) and a primitive root of that number. For example, let n equal 11. See that W(4,2)-length 4, 2 colors has 11 in parentheses. Let's use the primitive root 2. 2 is a primitive root of 11 because its powers up to 2^10 [2,4,8,16,32,64,128,256,512,1024] modulo 11 (the remainder when dividing by 11) are all distinct and equal [2,4,8,5,10,9,7,3,6,1] which we color red, blue, red, blue. Now all we have to do is reorder this is sequence, getting us [1,2,3,4,5,6,7,8,9,10]. It is proven that we can add the color 11, which should be blue. It is also proven that we can concatenate 3 more copies of this 11-term sequence while avoiding 4 evenly spaced of the same color. It is also proven we can add a 34th term, so we will. We have just found that W(4,2)-subsequence length 4, 2 colors equals 35. Note it does not equal 34 because this table shows the minimum length that guarantees an evenly spaced sequence of the same color, not the maximum length that can be reached without an evenly spaced sequence of the same color.
And there is a UK BOINC Team set up on there, with 2 members.
Hope you join :D
'UBT - Chris' is my old name - I now crunch as 'CaffeinatedSloth' but I'm still 100% UBT :D
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UBT - Timbo
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Post by UBT - Timbo » Thu Mar 19, 2015 9:43 pm

Hi all,

Well done Chris.

The project can be added to BOINC Manager by inputting this:
EXCEPT that overnight they've changed the URL - it is now:

regards
Tim

Woodles
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Post by Woodles » Fri Mar 20, 2015 8:59 am

Hi Chris,

Well spotted. I might give it a go once I've got UBT to UK number one in SRBASE :)

Mark
Last edited by Woodles on Fri Mar 20, 2015 1:20 pm, edited 1 time in total.
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UBT - Timbo
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Post by UBT - Timbo » Fri Mar 20, 2015 11:13 am

Woodles wrote:Hi Chris,

Well potted. I might give it a go once I've got UBT to UK number one in SRBASE :)

Mark
Hi all

And if anyone wants to help out on SRBase and join in then you need to use this URL:

http://srbase.myfirewall.org/sr5/create ... l=home.php

and enter the following invitation code:

pillepalle

so that an account is created on their website FIRST.

Then you can add it as a project in BOINC Manager, using the password you've chosen. :)

Don't try and add it the usual way, in BM, without using the above form first, as it won't work :(

regards

Tim
Last edited by UBT - Timbo on Fri Mar 20, 2015 7:35 pm, edited 1 time in total.

UBT - Chris
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Post by UBT - Chris » Fri Mar 20, 2015 5:51 pm

Thanks, Mark - I've got about 150 credits on it so far, and if you want, I can do a few WUs on SRBase over the weekend - I'm also investigating to see if VDWN will bring out an android/RPi app, so I can crunch for that project on there, and have SRBase running more long-term on my laptop...
'UBT - Chris' is my old name - I now crunch as 'CaffeinatedSloth' but I'm still 100% UBT :D
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UBT - Chris
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Post by UBT - Chris » Sat Mar 21, 2015 11:50 am

Since the URL change of the project, I haven't had much success with the project - I had over 500 download fails: http://www.123numbers.org/results.php?u ... e=6&appid=

Anyone know when this will get resolved?
'UBT - Chris' is my old name - I now crunch as 'CaffeinatedSloth' but I'm still 100% UBT :D
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UBT - Timbo
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Post by UBT - Timbo » Sun Mar 22, 2015 8:38 am

Hi Chris

It shouldn't make any difference that they changed the URL.

But, like you, I've returned WU's which have been either invalid or inconclusive.

So, I asked a question on their forum to Daniel, the admin and no doubt I'll get an answer at some point

http://www.123numbers.org/forum_thread.php?id=16

Until I do, I've suspended their WU's :(

regards
Tim

UBT - Chris
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Post by UBT - Chris » Sun Mar 22, 2015 9:14 am

Didn't think it would Tim, but it is very coincidental...

And I can't post on the forums - it just doesn't show up with a button to post or create my own thread, and I sent a PM to ask Daniel why that was, but he hasn't replied...
'UBT - Chris' is my old name - I now crunch as 'CaffeinatedSloth' but I'm still 100% UBT :D
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UBT - Timbo
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Re: Van Der Waerden Numbers

Post by UBT - Timbo » Sat Feb 13, 2021 1:53 pm

Hi all

It looks like this project is back up and running again (as of about 10 days ago).

If you want to add it to BOINC Manager, then here's the "Add URL" code:

Code: Select all

https://vdwnumbers.org/vdwnumbers
It's a CPU based project, so no current tasks that use GPUs.

regards
Tim

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