The number n! (n factorial) is the product of all numbers from 1 to n. For example, 4! = 1 • 2 • 3 • 4 = 24 and 7! = 1 • 2 • 3 • 4 • 5 • 6 • 7 = 5040. If n ≥ 2, show that all the numbers
n! + 2, n! + 3, n! + 4, ..., n! + (n − 1), n! + n
are composite numbers.
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