\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)..\left(2^{256}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{256}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right).....\left(2^{256}+1\right)\)
\(=.................................................\)
\(=2^{512}-1\)