Carol / Kynea Primes - Page 14

kar_bon · 2018-01-16, 09:33

Some hints:

The page edits at Wikipedia for Kynea number shows the table for general bases was added on 2017-09-14 including the value (26^215057+1)^2-2.
There's only an IP adress given no user. Looking at the users edits you'll find edits on a talk page.
At the bottom there's a big table of generalized repunits given. The same table can be found on MersenneWiki done by Sweety439.
So it's the question were those edits done by the same user?

I really want to create a Wiki for data tables like this, so every edit can be checked and verified by the admins. I also would only grant access to users with full name/user, in Wikipedia everybody can change pages without login, that's a real pity.

This Wiki could also handle reservations, everybody logged in can fill in their results and every edit can be seen and verified. All edits are on one page instead spreaded over many posts like a forum. Many pages like the search for Kynea primes could be managed and found on one data source. References are given also as links to other pages or data bases like OEIS.
I got more than 2 years experience with my Wiki for jigsaw puzzles now and there're 8,000 puzzle given with many data and pictures. None has done such data base before.
The problem with such number pages are the variety of numbers: Mersenne primes, Riesel/Proth primes, Home Primes, special primes like Kynea/Carol, Aliquot Seqs or other numbers are very different in display and search. I got some ideas but not yet real tested on this, because it takes much time to do.

gd_barnes · 2018-01-16, 22:09

Quote:

Originally Posted by kar_bon

Some hints:

The page edits at Wikipedia for Kynea number shows the table for general bases was added on 2017-09-14 including the value (26^215057+1)^2-2.
There's only an IP adress given no user. Looking at the users edits you'll find edits on a talk page.

Interesting. I wonder where the person who edited the page came up with that huge prime. Regardless, I have edited the Wiki to remove it. I also checked all of the other Kynea numbers shown there and they look good.

rogue · 2018-01-17, 00:15

Gary, don't you have anything better to do?

I believe that I have made all of the changes you have pointed out.

I don't know where that massive prime for b=26 came from. Some of the reservations are done via e-mail, so I won't remove them.

Batalov · 2018-01-17, 03:31

Quote:

Originally Posted by kar_bon

Some hints:

The page edits at Wikipedia for Kynea number shows the table for general bases was added on 2017-09-14 including the value (26^215057+1)^2-2...

...which is divisible by 7. Nice going!

Another example how in obscure areas Wikipedia is the last refuge of scoundrels.

gd_barnes · 2018-01-22, 08:47

I have made all of the corrections to Wikipedia as per my previous doublechecks. I also added new large base 2 primes that were previously found by Mark plus their corresponding base 4, 8, and 16 primes. See:

https://en.wikipedia.org/wiki/Carol_number
https://en.wikipedia.org/wiki/Kynea_number

Mark, you might want to update the integer sequences page here:
https://oeis.org/A091515

rogue · 2018-01-22, 19:16

Quote:

Originally Posted by gd_barnes

I have made all of the corrections to Wikipedia as per my previous doublechecks. I also added new large base 2 primes that were previously found by Mark plus their corresponding base 4, 8, and 16 primes. See:

https://en.wikipedia.org/wiki/Carol_number
https://en.wikipedia.org/wiki/Kynea_number

Mark, you might want to update the integer sequences page here:
https://oeis.org/A091515

Submitted

gd_barnes · 2018-01-29, 09:52

By luck in browsing around here I figured out the mystery surrounding the (26^215057+1)^2-2 "non-prime".

It was in an older thread in this subforum. See:
http://mersenneforum.org/showpost.ph...8&postcount=44

The prime is:
(26^75993+1)^2-2

Found by wombatman on 2016/07/02.

I doublechecked and verified that it is prime. This prime will need to be posted on the primes page. I have added it to Wikipedia.

Mark, I believe that you used the length of the prime (215057) as the exponent and then someone copied it over to Wikipedia at some point because it was found in 2016 but the primes were not added to Wiki until midway through 2017. Since this is the second time this has happened (also on base 640 for one found by Serge), I'm recommending that we not post the length of these primes.

LaurV · 2018-02-12, 09:24

Quote:

Originally Posted by gd_barnes

I have made all of the corrections to Wikipedia as per my previous doublechecks. I also added new large base 2 primes that were previously found by Mark plus their corresponding base 4, 8, and 16 primes. See:

https://en.wikipedia.org/wiki/Carol_number

In the Wiki page, section "primes and modular relations" it still says that the prime found in 2007 is "the largest known". This has to be reformulated somehow, to keep it (I am not for deleting any information with historical value), and add the fact that the largest prime known today is... larger. Or just say "see the table below" or something. Unfortunately my English level, and my knowledge about Carol primes are not developed enough to tickle this change by myself...

kar_bon · 2018-02-12, 10:53

I thinks it's not the purpose to Wikipedia to show/keep all historic finds of such primes. The biggest currently found should be good. For further information there're external links like the OEIS or PrimePages or condensed pages like those from Steven Harvey (March 2016) or Mark here.

The problem I see is every such page of Wikipedia for different languages has to keep current especially the table on that page.
I would prefer a section "Record" to hold the current record and a link to such a table. The table is independently updated by others working and searching those primes so best info available.

Other problems are the spreaded info: some pages and papers or many threads in forums holding historic data but none the whole info at once. Search limits are not easy to find or results or efforts are doubled (see other thread for Carol/Kynea).

I'm thinking and testing of a Wiki for such information: current and historic with all references you can find to make it easier for searchers, and easy to edit those pages to keep them current. Everyone could reserve ranges and update their results. Some first thoughts and implementations I've done but nothing to show yet.

gd_barnes · 2018-02-12, 18:09

I have updated the Wikis for both Carol and Kynea primes for the largest primes. It involved several changes to links and extraneous info. Feel free to check my changes:

https://en.wikipedia.org/wiki/Carol_number
https://en.wikipedia.org/wiki/Kynea_number

gd_barnes · 2018-02-13, 16:39

Base 42 is complete to n=30K. 2 new primes found n=10K-30K:

(42^10573-1)^2-2

(42^25002+1)^2-2

2018-01-22, 08:47	#148
gd_barnes May 2007 Kansas; USA 2²·19·137 Posts	I have made all of the corrections to Wikipedia as per my previous doublechecks. I also added new large base 2 primes that were previously found by Mark plus their corresponding base 4, 8, and 16 primes. See: https://en.wikipedia.org/wiki/Carol_number https://en.wikipedia.org/wiki/Kynea_number Mark, you might want to update the integer sequences page here: https://oeis.org/A091515 Last fiddled with by gd_barnes on 2018-01-22 at 08:52

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2018-01-16, 09:33	#144
kar_bon Mar 2006 Germany 2²×727 Posts	Some hints: The page edits at Wikipedia for Kynea number shows the table for general bases was added on 2017-09-14 including the value (26^215057+1)^2-2. There's only an IP adress given no user. Looking at the users edits you'll find edits on a talk page. At the bottom there's a big table of generalized repunits given. The same table can be found on MersenneWiki done by Sweety439. So it's the question were those edits done by the same user? I really want to create a Wiki for data tables like this, so every edit can be checked and verified by the admins. I also would only grant access to users with full name/user, in Wikipedia everybody can change pages without login, that's a real pity. This Wiki could also handle reservations, everybody logged in can fill in their results and every edit can be seen and verified. All edits are on one page instead spreaded over many posts like a forum. Many pages like the search for Kynea primes could be managed and found on one data source. References are given also as links to other pages or data bases like OEIS. I got more than 2 years experience with my Wiki for jigsaw puzzles now and there're 8,000 puzzle given with many data and pictures. None has done such data base before. The problem with such number pages are the variety of numbers: Mersenne primes, Riesel/Proth primes, Home Primes, special primes like Kynea/Carol, Aliquot Seqs or other numbers are very different in display and search. I got some ideas but not yet real tested on this, because it takes much time to do.

2018-01-17, 00:15	#146
rogue "Mark" Apr 2003 Between here and the 2·3²·353 Posts	Gary, don't you have anything better to do? I believe that I have made all of the changes you have pointed out. I don't know where that massive prime for b=26 came from. Some of the reservations are done via e-mail, so I won't remove them.

2018-01-29, 09:52	#150
gd_barnes May 2007 Kansas; USA 2²·19·137 Posts	By luck in browsing around here I figured out the mystery surrounding the (26^215057+1)^2-2 "non-prime". It was in an older thread in this subforum. See: http://mersenneforum.org/showpost.ph...8&postcount=44 The prime is: (26^75993+1)^2-2 Found by wombatman on 2016/07/02. I doublechecked and verified that it is prime. This prime will need to be posted on the primes page. I have added it to Wikipedia. Mark, I believe that you used the length of the prime (215057) as the exponent and then someone copied it over to Wikipedia at some point because it was found in 2016 but the primes were not added to Wiki until midway through 2017. Since this is the second time this has happened (also on base 640 for one found by Serge), I'm recommending that we not post the length of these primes.

2018-02-12, 10:53	#152
kar_bon Mar 2006 Germany 2²·727 Posts	I thinks it's not the purpose to Wikipedia to show/keep all historic finds of such primes. The biggest currently found should be good. For further information there're external links like the OEIS or PrimePages or condensed pages like those from Steven Harvey (March 2016) or Mark here. The problem I see is every such page of Wikipedia for different languages has to keep current especially the table on that page. I would prefer a section "Record" to hold the current record and a link to such a table. The table is independently updated by others working and searching those primes so best info available. Other problems are the spreaded info: some pages and papers or many threads in forums holding historic data but none the whole info at once. Search limits are not easy to find or results or efforts are doubled (see other thread for Carol/Kynea). I'm thinking and testing of a Wiki for such information: current and historic with all references you can find to make it easier for searchers, and easy to edit those pages to keep them current. Everyone could reserve ranges and update their results. Some first thoughts and implementations I've done but nothing to show yet.

2018-02-12, 18:09	#153
gd_barnes May 2007 Kansas; USA 2²·19·137 Posts	I have updated the Wikis for both Carol and Kynea primes for the largest primes. It involved several changes to links and extraneous info. Feel free to check my changes: https://en.wikipedia.org/wiki/Carol_number https://en.wikipedia.org/wiki/Kynea_number

2018-02-13, 16:39	#154
gd_barnes May 2007 Kansas; USA 2²·19·137 Posts	Base 42 is complete to n=30K. 2 new primes found n=10K-30K: (42^10573-1)^2-2 (42^25002+1)^2-2