Prove that 10^100+1 is not the smallest prime greater than googol.
Hello, meshel88!
Prove that $\displaystyle 10^{100}+1$ is not the smallest prime greater than googol.
Fact: .$\displaystyle 10^{100}+1$ is a composite.
Proof: .$\displaystyle 10^{100}+1 \;=\;\left(10^{20}\right)^5 + 1^5 \;=\; \left(10^{20}+1\right)\left(10^{80} - 10^{60} + 10^{40} - 10^{20} + 1\right)$