Greater than 2
Insufficient information
$0$
$1$

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Every number in the sequence can be factorized. The sequence can be rewritten as

$2016!+2, 2016!+3, ..., 2016!+2016\\2(\frac {2016!}{2}+1), 3(\frac{2016!}{3}+1), ... 2016(\frac {2016!}{2016}+1)$