Thread: Octoproths
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Old 2005-04-05, 21:53   #1
robert44444uk
 
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Jun 2003
Oxford, UK

35578 Posts
Default Octoproths

I am posting this again for those looking for a challenge - but this time in the Maths thread:

Try to find the smallest and largest integer (maybe larger than you think) k*2^n+1 such that:

k*2^n+1, k*2^n-1, k*2^(n+1)+1, k*2^(n+1)-1, 2^n+k, 2^n-k, 2^(n+1)+k,
2^(n+1)-k, all probable prime

I have called these octoproths. On the large side of things, I have looked at n=32 and 1<k<4 billion and found only 6, with the following k values:

409668105
664495755
2368386195
2709707805
3383804865
3692088225

Interestingly, but not surprisingly these k are all multiples of k=105
(3*5*7) as this is a requirement for bitwins (I think). And therefore of interest to 15k searchers.

I have no idea about the smallest octoproths.

The really interesting thing about these groups is that it combines twins, Cunninghams and Payam Samidoost's observation about 2^n+/- k, these have the same covering sets as their Proth equaivalents.

Watch out for negative values, because 2^n-k can be really small

Regards

Robert Smith
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