What is the Least Prime Factor of $3^{3241} + 8^{2433}$

Question

I'm not sure how to do this question

Attempt $$3^{3241} + 8^{2433}$$ I start by taking this number mod 3 $$3^{3241} + 8^{2433} \equiv 8^{2433} \mod 3$$ No we can see that $8^2 \equiv 1 \mod 3$. So $$8^{2433} \equiv 8 * (8^2)^{1216} \equiv 8 * 1^{1216} \equiv 8 \equiv 2 \mod 3$$

Ok So I know that the number is 2 mod 3. Therefore, it doesn't divide 3. I need to find the smallest prime number that will divide the number. Where do I go from here?

Thanks SE

Answer 1

A quick python script shows that $4283$ is a divisor of this number, and is the smallest non-trivial divisor.

Wolfram|Alpha also gives this factor, and stops there.

Answer 2

By running the following program, the first prime that divides x can be found.

x = 3**3241 + 8**2433
i = 2
while x % i != 0:
    i += 1
print(i)

>> 4283

Although I was going to post it as a comment, I wanted to show my code used to retrieve the answer which cannot be posted in a comment. It should also be noted that $4283$ cannot be written as $3^i + 8^j$ for integers $i$ and $j$.