Let p1, p2,…,pn be the first n primes and let m be an integer with 1 < m < n. Let Q be the product of a set of m primes in the list and let R be the producl of the remaining primes. Show that Q + R is not divisible by any primes in the list, and hence must have a prime factor not in the list. Conclude that there are infinitely many primes.
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