Prolific power primes

[Ed Pegg]

I started a look at primes of the form a^n + b, trying to
find (a,b) pairs that seemed to surpass (2,-1).  One of 
the best that I found was (3,10I).  

3^n + 10I   (32 under 10000)
1, 2, 3, 4, 5, 9, 12, 13, 27, 45, 78, 86, 115, 131, 172, 203,
278, 315, 322, 489, 589, 884, 1181, 1289, 1362, 1402, 1464, 
1541, 1601, 1638, 6018, 7640

2^n - 1  (22 under 10000)
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279,
2203, 2281, 3217, 4253, 4423, 9689, 9941

--Ed Pegg Jr.