1989 AMC 8 第 16 题

先试着解答 1989 AMC 8 第 16 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1989 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

16.

4747 可以用多少种方式写成两个质数的和?
In how many ways can 4747 be written as the sum of two primes?
00
11
22
33
多于 33
more than 33
答案:A
知识点:质数奇偶性
小提示:
4747 是奇数,所以两个质数中必须有一个是偶数
4747 is odd, so one of the two primes must be even
大提示:
唯一的偶质数是 22,这会迫使另一个数是 4545。
The only even prime is 2,2, which would force the other prime to be 4545
解答:
因为 4747 是奇数,若两个质数的和等于 4747,其中必有一个偶质数。唯一的偶质数是 22。
于是另一个数必须是 47−2=4547 - 2 = 45,但 45=9×545 = 9 \times 5,不是质数。因此没有这样的表示方式。
所以正确答案是 A。
Since 4747 is odd, a sum of two primes equal to 4747 needs one even prime and one odd prime. The only even prime is 2.2.
That would require the other number to be 47−2=45,47 - 2 = 45, but 45=9×545 = 9 \times 5 is not prime. So there is no way.
Thus, the correct answer is A .
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