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Since xab−1=(xa−1)×(xa(b−1)+xa(b−2)+⋯+xa+1) x ^ { ab } - 1 = (x^a -1 ) \times \left( x^{ a (b-1) } + x^ { a (b-2) } + \cdots + x^ a + 1 \right) xab−1=(xa−1)×(xa(b−1)+xa(b−2)+⋯+xa+1), we conclude that the number 2105−1 2^ {105} -1 2105−1 has factors of 23−1=7 2^3 - 1 = 7 23−1=7, 25−1=31 2^5 - 1 = 31 25−1=31 and 27−1=127 2^{7} - 1 = 127 27−1=127. Is 2105−1(23−1)×(25−1)×(27−1) \frac{ 2 ^ { 105} - 1 } { \big( 2^3 -1 \big) \times \big( 2^5 -1 \big) \times \big(2 ^ 7 -1 \big) } (23−1)×(25−1)×(27−1)2105−1 prime?
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