Quote:
Originally Posted by Kosmaj
I define (k,n) to be DodecaProth if both (k,n) and (k,n+1) are OctoProths.

What a nice definition!
Probably it is also possible to write a GMP program for this search, like for octoproth.
Sometime before I thought to define ....proth ( what is the correct name for sixteen? ), where (k,n) and (k,n+2) are Octoproths ( this means that this is also a DodecaProth because it is easy to prove that if (k,n) and (k,n+2) are Octoproths then (k,n+1) is also an octoproth ).
It means 16 primes, but today to find such a pattern is impossible, even by a fast sieve and fast prp checking.
Ps. Searching for Dodecaproth would be faster for a given n value and a given Range than searching for Octoproths. You don't need to find all octoproths in that range!