+486 What is the units digit of $2^{2^{1000}}+1$(The $1000^{th}$ Fermat prime)?
+600 Note that $2^{13}\equiv 2^1\pmod{10}$ so $2^{n}=2^{n+12}\pmod{10}$. Then $2^{1000}\equiv 4\pmod{12}$ so $2^{2^{1000}}\equiv 2^4\equiv 6\pmod{10}$. The answer is $6+1=7$.
