Thread: Octoproths
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Old 2005-04-16, 13:56   #53
axn's Avatar
Jun 2003

22·7·179 Posts

Originally Posted by Dougy
So, if my program works properly, there are no (certified prime) octoproths within the ranges n=31-50 and k=15-21207165.

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 k-value 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 31-50 for k < 10^7. I am right now in the process of checking whether 21207165 is the smallest possible for n <= 1000
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