4. Given that $7,999,999,999$ has at most two prime factors, find its largest prime factor.
Solution: $7,999,999,999=8 \cdot 10^{9}-1=2000^{3}-1=(2000-1)\left(2000^{2}+2000+1\right)$, so $\left(2000^{2}+2000+1\right)=4,002,001$ is its largest prime factor.