Clausen Factorization For The sixth Fermat number

 

$$\begin{array}{l}\\ F_6=2^{64}+1=2^{48}\ast 2^{16}+1\\ \\ =281474976710656\ast 2^{16}+1\\ \\ =281473950092895\ast 2^{16}+1026617761\ast 2^{16}+1\\ \\ =1071\ast 262814145745\ast 2^{16}+2628141456816\ast 2^8+1\\ \\ =1071\ast 262814145745\ast 2^{16}+\left(1071+262814145745\right)\ast 2^8+1\\ \\ =\left(1071\ast 2^8+1\right)\left(262814145745\ast 2^8+1\right)\\ \\ =274177\ast 67280421310721.\end{array}$$