Quote:
Originally Posted by Dougy
So, if my program works properly, there are no (certified prime) octoproths within the ranges n=3150 and k=1521207165.
Furthermore
328724235 29
233752995 30
are the only octoproths with those bases.
So this is a proof that
21207165*2^28+1 = 5692755007242241.
109989075*2^27+1 = 14762483751321601.
are the smallest two octoproths.
Also 21207165 is also the smallest known kvalue forming a octoproth. I wonder if it's actually the smallest possible. I might search with a fixed k and varying n instead. (but that'd require writing a whole new program)
It would be nice if someone could verify this independently before I submit it anywhere.

I have verified that there are no octo's between 10 <= n <= 26. Also there are no octo's in the range 3150 for k < 10^7. I am right now in the process of checking whether 21207165 is the smallest possible for n <= 1000