Thread: Octoproths
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Old 2005-04-16, 01:20   #49
Dougy
 
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Aug 2004
Melbourne, Australia

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

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 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.
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