Searched (probable) primes of the form (b+1)^p-b^p for b = 151 to 160. (Curremtly at n=26K)
For b = 151, I found p = 59, 71, 4583, 26029.
For b = 152, I found p = 1583.
For b = 153, I found p = 2, 3.
For b = 154, I found p = 43, 587, 883.
For b = 155, I found p = 2, 7, 467, 859, 3169.
For b = 156, I found p = 2, 3, 7, 17, 661.
For b = 157, I found p = 3, 37, 61.
For b = 158, I found p = 2, 3, 17, 107, 13313.
For b = 159, I found p = 7, 379, 661, 5521.
For b = 160, I found p = 13, 31, 151.
To be completed...