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^n1, k*2^(n+1)+1, k*2^(n+1)1, 2^n+k, 2^nk, 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^nk can be really small
Regards
Robert Smith
