What's the missing number in the following sequence?
2, 6, 30, 210, ?, 30030, 510510, ...
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Let a term before 2 be a 0 = 1 , then the following terms for n ≥ 1 are given by a n = a n − 1 p ( n ) where p ( n ) is the n t h prime number. Therefore, we have:
a 1 a 2 a 3 a 4 a 5 a 6 a 7 = a 0 × p ( 1 ) = 1 × 2 = a 1 × p ( 2 ) = 2 × 3 = a 2 × p ( 3 ) = 6 × 5 = a 3 × p ( 4 ) = 3 0 × 7 = a 4 × p ( 5 ) = 2 1 0 × 1 1 = a 5 × p ( 6 ) = 2 3 1 0 × 1 3 = a 6 × p ( 7 ) = 3 0 0 3 0 × 1 7 = = = = = = = 2 6 3 0 2 1 0 2 3 1 0 3 0 0 3 0 5 1 0 5 1 0