All of the options (A, C, D, and E) are multiple of 2:

8p = 2 * 4p
8p + 2 = 2 * (4p + 1)
8p + 4 = 2 * (4p + 2)
8p + 6 = 2 * (4p + 3)

Hence, they cannot be prime numbers (since prime numbers must only be divisible by 1 and itself)

Only option B: 8p + 1 does not apparently have any factors
Thus, it is the only one that CAN BE prime (it might not be prime as well - we cannot ensure that it is prime)

Option B

8p = even integer
even + odd = odd
8p + 1 = odd integer

Answer B is the only choice that leads to an odd integer.

Also, 8(5) + 1 = 41
41 is a prime number