Also another interesting problem if anyone's interested:

Twin primes of the form k*b^n+-1 with k < n -->

Due to the limited choices of fixing only base b, there are extremely rare. I tested some bases (3, 5, 6, 7, 10, 11, 12). Here are the largest twins found to n=2K (except b=3, which is checked to n=10K). Quite small, I tell you:

Second twin (p+2):

Code:

2618*3^4286+1
336*5^765+1
613*6^1922+1
525*10^632+1
1182*11^1409+1
860*12^967+1

I didn't find any for base 7, although I'm sure they exist. The idea is that if k < n, we can get k as small as possible, so if all bases < 100 were tested, odds are you'll find a twin with a very small k. Continuing on with the search.