Prime Constellations

[kar_bon]

I mailed T.Forbes some values not mentioned on his page in March 2012:

Under "First appearance of 100 digits" for k=2 (Twin), found by me:
10^99+6001 and 10^99+6003

Also there're smaller ones under "First appearance of 10000 digits" k=2, see Top5000:
93675195*2^33250-1 / +1 : 10018 digits (instead his listed 11713 digits) so far

Same for "First appearance of 1000 digits" k=2, see Top5000:
10^999+1975081 / +1975083 : 1000 digits (instead his listed 1040 digits)

[MattcAnderson]

I'm glad to see that a few people are interested in this project. Someone else may want to find examples of 13-tuples, if not, I will do it. In my humble opinion, the OEIS is a good place for that data.

Regards,
Matt

[science_man_88]

Originally Posted by MattcAnderson

I'm glad to see that a few people are interested in this project. Someone else may want to find examples of 13-tuples, if not, I will do it. In my humble opinion, the OEIS is a good place for that data.

Regards,
Matt

using pari and primes>3 I get 5,7,11,13,17,19,23,29,31,37,41,43,47-> p,p+2,p+6,p+8,p+12,p+14,p+18,p+24,p+26,p+32,p+36,p+38,p+42 as the lowest amount below the 100th prime. 47-5 =42 but this appears to be a 12-tuplet according to the minimums listed so it must not count the opening prime or something that I'm missing like repeatable across all the primes.

edit: yep that's likely the problem.

[Jens K Andersen]

Originally Posted by kar_bon

I mailed T.Forbes some values not mentioned on his page in March 2012

In those tables he shows the first appearance to be discovered and not the smallest appearance.

[Jens K Andersen]

Originally Posted by MattcAnderson

Someone else may want to find examples of 13-tuples, if not, I will do it.

There are 20 or 21 examples of each pattern in http://anthony.d.forbes.googlepages.com/ktmin.txt

[Jens K Andersen]

Originally Posted by MattcAnderson

The Onlie Encyclopedia of Integer Sequences has refereed and accepted some of my work.

https://sites.google.com/site/primeconstellations/

I have confirmed the 52 smallest 12-tuplets in http://oeis.org/A213601.
It took 10 minutes with my tuplet finder in C on a 2.4 GHz Core 2 Duo.

[henryzz]

Originally Posted by Jens K Andersen

I have confirmed the 52 smallest 12-tuplets in http://oeis.org/A213601.
It took 10 minutes with my tuplet finder in C on a 2.4 GHz Core 2 Duo.

Is this program publicly available?

[Jens K Andersen]

Originally Posted by henryzz

Is this program publicly available?

No. The source is adapted for each run. I sometimes mail a version for a specific purpose like breaking a tuplet or Cunningham chain record.

[MattcAnderson]

Prime 13 tuplets of the 1st kind have been accepted by the Online Encyclopedia of integer sequences.

https://oeis.org/A214947

[ET_]

Luigi

[henryzz]

Originally Posted by Jens K Andersen

No. The source is adapted for each run. I sometimes mail a version for a specific purpose like breaking a tuplet or Cunningham chain record.

Shame. Several people on mersenneforum aren't adverse to making minor changes to code for each run. See http://mersenneforum.org/showthread.php?t=16705&page=2