My little prime factors

It is known that if $n$ is a positive odd integer $\Rightarrow\ a+b|a^n+b^n$

Write $2^{30}+3^{30}$ as an expression with odd exponents.

$2^{30}+3^{30}=4^{15}+9^{15}=(4^3)^5+(9^3)^5=(4^5)^3+(9^5)^3 \Rightarrow 4+9,4^3+9^3,4^5+9^5$ divide $2^{30}+3^{30}$ , so one of the two prime factors searched is $13$ . To find the other apply divisibility rules to:

$4^3+9^3=793=13\times 61$

$4^5+9^5=60073=13\times4621$

tTe two prime factors of two digits are $13$ and $61$ , $\therefore$ its sum is $\boxed{74}$