AMC 8 1987 Problem 20
AMC8 1987 年第 20 题
整除与因数★★★☆☆
"If a whole number is not prime, then the whole number n-2 is not prime." A value of which shows this statement to be false is
"如果一个正整数 不是质数，则正整数 n-2 也不是质数。" 以下哪个 的值能证明该陈述为假？
- A.9
- B.12
- C.13
- D.16
- E.23
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
A counterexample to this statement is a non-prime number such that n-2 is prime. So 13 and 23 are not counterexamples since they are prime, while 12 and 16 are not counterexamples since 10 and 14 are not prime. Only 9 is such a counterexample, since 9 is not prime but 9-2 = 7 is.
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