Van Der Waerden Numbers

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Van Der Waerden Numbers

Post by Contact »

The previous 24 hours has seen large updates to the website. Many pages are working and I am able to log into my account. The BOINC client only partially attaches with a warning that the feeder isn't running, so there is much work left to be done, but it looks good so far.

http://www.vdwnumbers.org/vdwnumbers/

The project has been dormant for many years after it's first run but then this post on December 29 2020
http://www.vdwnumbers.org/vdwnumbers/fo ... .php?id=80
Daniel Monroe - vdwnumbers.org Project Administrator wrote:This project is in the process of being revived in light of comments I have received that optimal primes for two colors and large lengths exhibit strange properties. In particular, the best primes for lengths 23, 24, and 25 are one more than 6 * p, 4 * 47 * p, and 2 * 24 * p, the ps all being primes. Striking in particular is the multiplicative composition of the latter two; 24 = 25 - 1 and 47 = 2 * 24 - 1.

Loop unrolling, faster progression checking, and bit packing have made for a much faster program, making it feasible to run the two-color case up to 4 billion. The computation should give insight into:

The growth of low-color, high-length van der Waerden numbers
The additive distribution of quadratic residues modulo a prime
Note: this project is no longer generating work. Van Der Waerden Numbers is a research project that uses Internet-connected computers to find better lower bounds for these numbers.

Background
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. See a table of the results so far below.

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]. We can add the color 11, which should be blue. Rabung proved that under certain conditions we can concatenate 3 more copies of this 11-term sequence while avoiding 4 evenly spaced of the same color. We can add a 34th term, so we will. The existence of this sequence of 34 proves that W(4,2) is more than 34.

BOINC Synergy: http://www.vdwnumbers.org/vdwnumbers/te ... ?teamid=13

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Re: Van Der Waerden Numbers

Post by Contact »

http://www.vdwnumbers.org/vdwnumbers/
Just started downloading, returning and validating many, many, very, very short wu's. Most of the website works other than posting to forums.
The site blew up for a short while with
browser wrote:This site can’t be reached www.vdwnumbers.org refused to connect.
Seems to be fairly stable though, even with a blistering pace of small packets of data going up and down the pipe.


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Re: Van Der Waerden Numbers

Post by Contact »

I've just received this communication from the project admin:
Daniel wrote:Thanks for relaying this message to us! Unfortunately, the project is still not working, and we've been having issues with the server upgrade that are messing with the user data (everything is backed up, of course). It looks like we were not clear enough that things are under reconstruction, and we apologize for any frustration this might have caused. We're working around the clock to get everything running again, but for now it looks like we might temporarily shut down the site in order not to create any more confusion.

Best wishes,
Daniel
There was an upgrade a few hours ago that caused several database errors to show on the site, broken or deprecated links, no teams, etc. We've seen this before on other projects attempting that upgrade so I'm sure it will be eventually sorted out.


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Re: Van Der Waerden Numbers

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A new message on the home page
Van Der Waerden Numbers wrote:PLEASE NOTE THAT THIS PROJECT IS CURRENTLY NOT OPERATIONAL. THE LOG-IN AND MESSAGE BOARD FEATURES ARE TEMPORARILY DOWN, AND THE PROJECT IS ONLY GENERATING DUMMY WORK. PLEASE CLICK HERE TO MONITOR OUR PROGRESS AS WE GET EVERYTHING RUNNING AGAIN. THANK YOU FOR YOUR PATIENCE.
One of the most interesting cards in the link above:
https://trello.com/c/NEPZ5aaO


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Re: Van Der Waerden Numbers

Post by Contact »

It's very good to see that Create new BOINC project card has been moved to Done along with the Fix e-mail issue card.


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Re: Van Der Waerden Numbers

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It's official. BOINC Synergy welcomes Van Der Waerden Numbers to it's return to Alpha Test stage.
http://www.vdwnumbers.org/vdwnumbers/fo ... postid=389

Also great to see that stats export is working and has been approved for public display.
:W


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Re: Van Der Waerden Numbers

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The project has found its first new lower bound! The best length-25 prime has increased from 958,485,937 to 987,469,279. I still believe that this can be further improved.
____________
Daniel Monroe
vdwnumbers.org Project Administrator
http://www.vdwnumbers.org/vdwnumbers/fo ... .php?id=79


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kraDen
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Re: Van Der Waerden Numbers

Post by kraDen »

Is the Van Der Waerden Numbers project broken?
when I trry to log in I get (similar errors occur when browsing the project site e.g. http://www.vdwnumbers.org/server_status.php)
Warning: mysqli::mysqli(): (HY000/2002): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) in /home/boincadm/projects/vdwnumbers/html/inc/db_conn.inc on line 39

Warning: mysqli::query(): Couldn't fetch mysqli in /home/boincadm/projects/vdwnumbers/html/inc/db_conn.inc on line 63
Database Error

Warning: mysqli::escape_string(): Couldn't fetch mysqli in /home/boincadm/projects/vdwnumbers/html/inc/db_conn.inc on line 227

Warning: mysqli::query(): Couldn't fetch mysqli in /home/boincadm/projects/vdwnumbers/html/inc/db_conn.inc on line 63
Database Error
No such account

Warning: mysqli::escape_string(): Couldn't fetch mysqli in /home/boincadm/projects/vdwnumbers/html/inc/db_conn.inc on line 227
log in
No account with email address kenjdavis@gmail.com exists. Please go back and try again.


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Re: Van Der Waerden Numbers

Post by Contact »

kraDen wrote: Sun Sep 05, 2021 10:37 pm Is the Van Der Waerden Numbers project broken?
Right now the project has database errors. I think I remember seeing a full disk notice in the BOINC Manager just before the errors.


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