Pretty Large

Since xab1=(xa1)×(xa(b1)+xa(b2)++xa+1) x ^ { ab } - 1 = (x^a -1 ) \times \left( x^{ a (b-1) } + x^ { a (b-2) } + \cdots + x^ a + 1 \right) , we conclude that the number 21051 2^ {105} -1 has factors of 231=7 2^3 - 1 = 7 , 251=31 2^5 - 1 = 31 and 271=127 2^{7} - 1 = 127 . Is 21051(231)×(251)×(271) \frac{ 2 ^ { 105} - 1 } { \big( 2^3 -1 \big) \times \big( 2^5 -1 \big) \times \big(2 ^ 7 -1 \big) } prime?

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