Some maths
If k*2^n+1 is an octoproth then
k = 1 mod 2. If k is even then 2^(n+1) + k is divisible by 2.
k = 0 mod 3. If k = 1 mod 3 then either 3 divides k*2^n+1 or k*2^(n+1)+1. Similarly for k = 2 mod 3
k = 0 mod 5.
k = 0 mod 7 or (n = 1 mod 3 and k = +/ 1 mod 7).
I can't make any other useful criteria from any other primes. Does anybody know of other goodies like this?
