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Unformatted text preview: 5,. ..,k? Go the easy route and take N = k!. Clearly, then, k! + 2, k! + 3, k! + 4,. .., k! + k are all composite numbers. These observations give one way of &quot;constructing&quot; new primes. Suppose you have a collection of primes, say, p 1 , p 2 ,..., p t . Then the number p 1 p 2 ...p t + 1 must contain a &quot;new&quot; prime not in your set (in fact, usually a big one) as a factor. Although I wouldnt recommend it as an efficient way of locating primes, its a way which is guaranteed to work....
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