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November 14, 2013

Consecutive composite integers

Given any integer n \ge 2 , we can always find an integer m such that each of the n-1 consecutive integers m + 2, m + 3,..., m + n are composite.

True

Discussion:

Take m=n!. Then the consecutive integers n! + 2 , n! + 3 , ... n! + n are all composite.

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