Which of the following cannot be expressed as the sum of two prime numbers?

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问题 Which of the following cannot be expressed as the sum of two prime numbers?

选项 A、21
B、14
C、18
D、28
E、23

答案E

解析这道题目用排除法当然可以迅速解出来，比如：21=19+2，14=7+7，18=13+5，28=23+5，只剩下23，当然选择E。但是如果利用上面的定理，则速度更快。五个选项中B、C、D都为大于2的偶数，根据定理必然可以表达为两个质数的和；剩下选项A、E均为奇数，若两数相加为奇数，则这两数必然为一奇一偶。而这个数又要能够表达为两个质数的和，那么必须这一奇一偶都为质数，我们知道在所有质数中2是唯一的一个偶数，因此若A或E能够表达为两质数的和，其中一个一定为2，选项A：21-2=19，E：23-2=21，19为质数，21=3×7不为质数，因此E是正确答案。

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