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SOLVED:Fill in any missing details in this sketch of a proof of the infinitude of primes: Assume that there are only finitely many primes, say p1, p2, …, pn. Let A be the product of any r of these primes and put B=p1 p2 ⋯pn / A. Then each pk divides either A or B, but not both. Because A B>1, A B has a prime divisor different from any of the pk, which is a contradiction.
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