Question

$10001$ 可以用多少种方式写成两个质数之和？

In how many ways can $10001$ be written as the sum of two primes?

$0$

$1$

$2$

$3$

$4$

答案：A

知识点：奇偶性质数

难度评级：1200

解答：

两个数相加得到奇数时，一个必须是奇数，另一个必须是偶数。唯一的偶质数是 $2$ ，所以另一个数只能是 $9999$ 。但 $9999$ 不是质数，因此 $10001$ 不能写成两个质数之和。

所以正确答案是 A。

For two numbers to add to an odd number, one of them must be odd and the other even. Thus the only even prime is $2,$ so the other number is forced to be $9999.$ $9999$ is not prime, however, so $10001$ cannot be written as the sum of two primes.

Thus, A is the correct answer.

2011 AMC 8 第 24 题

答案：A

难度评级：1200

解答：

其他年份的第 24 题