What is the smallest prime divisor of 3^{11} + 5^7 + 1?
Oh ok, not that hard. \(3^{11}+5^7+1=255273\)
It's divisible by 3 because: \(2+5+5+2+7+3=24\)
and 24 is divisible by 3. So the answer is \(\boxed{3}.\)