2016 AMC 12A 第 5 题

Question

Goldbach 猜想指出：每个大于

2

的偶整数都可以写成两个质数之和，例如

2016=13+2003

。到目前为止，还没有人能证明该猜想为真，也没有人找到反例证明它为假。一个反例应当是什么？

Goldbach’s conjecture states that every even integer greater than

2

can be written as the sum of two prime numbers (for example,

2016=13+2003

). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?

一个大于

2

且可以写成两个质数之和的奇整数

an odd integer greater than

2

that can be written as the sum of two prime numbers

一个大于

2

且不能写成两个质数之和的奇整数

an odd integer greater than

2

that cannot be written as the sum of two prime numbers

一个大于

2

且可以写成两个非质数之和的偶整数

an even integer greater than

2

that can be written as the sum of two numbers that are not prime

一个大于

2

且可以写成两个质数之和的偶整数

an even integer greater than

2

that can be written as the sum of two prime numbers

一个大于

2

且不能写成两个质数之和的偶整数

an even integer greater than

2

that cannot be written as the sum of two prime numbers

答案：E

知识点：反例逻辑推理

难度评级：1100

小提示：

反例要满足命题的前提，但破坏结论。

A counterexample keeps the hypothesis but breaks the conclusion

大提示：

前提是“大于

2

的偶整数”；结论是“可以写成两个质数之和”。

The hypothesis is “even integer greater than

2

”; the conclusion is “a sum of two primes”

解答：

反例必须满足“大于

2

的偶整数”这个前提，同时不满足“可以写成两个质数之和”这个结论。

所以正确答案是 E。

A counterexample must satisfy the hypothesis of being an even integer greater than

2

while failing the conclusion that it can be written as the sum of two prime numbers.

Thus, the correct answer is E.

2016 AMC 12A 第 5 题

答案：E

难度评级：1100

小提示：

大提示：

解答：

其他年份的第 5 题