8. It is known that 999973 has exactly three distinct prime factors. Find the sum of these prime factors.
(1 mark)已知 999973 剛好有三個不同的質因數。求這些質因數之和。
8. 171
8. We have
$$
\begin{aligned}
999973 & =1000000-27 \\
& =100^{3}-3^{3} \\
& =(100-3)\left(100^{2}+100 \times 3+3^{2}\right) \\
& =97 \times 10309 \\
& =97 \times 13 \times 793 \\
& =97 \times 13^{2} \times 61
\end{aligned}
$$
and so the answer is $97+13+61=171$.