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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