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2019 AMC 12B Problem 2

Problem 2 of 25EasierNumber Theory

Consider the statement, “If nn is not prime, then n−2n-2 is prime.” Which of the following values of nn is a counterexample to this statement?

Answer choices

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Solution

A counterexample needs nn not prime (so the hypothesis holds) and n−2n-2 not prime (so the conclusion fails). Among the choices, 2727 is not prime and 27−2=2527-2=25 is not prime. The primes 1111 and 1919 fail the hypothesis, and 15−2=13,15-2=13, 21−2=1921-2=19 are prime. Thus, E is the correct answer.

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Concepts: counterexample · prime

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.