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Consecutive Composites

Problem

Although there are infinitely many primes it is a most remarkable fact that there can always be found a sequence of $n$ consecutive composite numbers. For example, there are thirteen consecutive composite numbers between the primes 113 and 127.

Prove that there exists a sequence of $n$ consecutive composite numbers for any finite value $n$.

Problem ID: 325 (26 Jun 2007)     Difficulty: 3 Star

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