> is there a prime 6-tuplet greater than 5...19 (length=14)?

No. Any 6-tuple of length 14 will have at least one

number which is divisible by 2, 3 or 5.

See http://anthony.d.forbes.googlepages.com/ktpatt.txt

and http://www.opertech.com/primes/k-tuples.html

for the densest admissible k-tuple patterns.

"Prime 6-tuplet" often refers to 6 primes in the densest

admissible pattern. The largest known are at

http://anthony.d.forbes.googlepages.com/ktuplets.htm

(5, 7, 11, 13, 17, 19) is inadmissible because all 5 values

modulo 5 are present.

--

Jens Kruse Andersen