3^11 and 5^13 are both the product of odd numbers,
so they are both odd
So 3^11 + 5^13 is the sum of two odd numbers and
is therefore even.
Any even number is divisible by 2. Therefore 2 is the smallest prime
that divides 3^11 + 5^13. [In fact, 2 is the
smallest prime, period!]..