1987 AMC 12 第 3 题

Question

小于

100

且个位数字为

7

的质数有多少个？（假设采用通常的

10

进制表示。）

How many primes less than

100

have

7

as the ones digit? (Assume the usual base

10

representation.)

4

5

6

7

8

列出所有小于

100

且个位数字为

7

的正整数

List every positive integer below

100

whose ones digit is

7

检验小于

100

的数是否为质数时，只需试除不超过其平方根的质数

For numbers below

100,

trial division only requires primes through their square roots

这些质数为

7,\ 17,\ 37,\ 47,\ 67,\ 97\text{。}

其余候选数

27,57,77

和

87

均为合数。因此，这样的质数共有

6

个。

所以正确答案是 C。

The primes are

7,\ 17,\ 37,\ 47,\ 67,\ 97.

The other candidates are composite:

27,57,77,

and

87.

Hence there are

6

such primes.

Thus the correct answer is C.

其他年份的第 3 题