Clausen Factorization For The sixth Fermat number

 

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