请问一个 prime factor 的问题？

正的偶整数n, 函数f(n)定义成所有from 2 to n 的正的偶整数的乘积， 那f(100)+1的最小的prime factor是什么：

a. bwteen 2 and 10

b. between 10 and 20

c. between 20 and 30

d. between 30 and 40

e. >40

是prep上的，头大，搞不出。

谢谢了。

这个题从TESTMAGIC上找到解法

f(100)=(2^50)*(50!)+1

Note that product has as factors all numbers from 1 to 50 so h(100)+1 will NOT be divisible by any of those since the remainder would be 1. So smallest prime factor has got to be more than 50. Answer is E.