Question

两个质数之和为 $85$ 。这两个质数的乘积是多少？

The sum of two prime numbers is $85.$ What is the product of these two prime numbers?

$85$

$91$

$115$

$133$

$166$

两个质数之和为奇数时，必须包含唯一的偶质数

An odd sum of two primes must include the only even prime.

从 $85$ 中减去那个偶质数

Subtract that even prime from $85$ .

两个奇质数之和是偶数。因为 $85$ 是奇数，所以其中一个质数必须是唯一的偶质数 $2$ 。

另一个质数是 $85-2=83$ ，所以乘积为 $2\cdot83=166$ 。

所以正确答案是 E。

The sum of two odd primes is even. Since $85$ is odd, one of the primes must be the only even prime, $2$ .

The other prime is $85-2=83$ , so the product is $2\cdot83=166$ .

Thus, E is the correct answer.