模考遇到一道不会的数学题，望童鞋们指教

verylotus

For every positive even integer n，the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of  h(100)+1 , then p is___

A between 2 to 10

B between 10 to 20

C between 20 to 30

D between 30 to 40

E greater than 40

答案是E    不会做，大家帮帮忙吧，遇到与质数有关的题目头就晕，这类题有什么技巧吗？

谢谢大家了！！

sophie177

h(100)=2*4*6*8*...100=2^50*(1*2*3*4*...50) 说明h(100)可以被1-50中的任何一个数整除.那么h(100)+1之后,被2-50的任何一个数整除后都会余1,所以它的最小质因子不可能是50之内的.

verylotus

明白了，太感谢了！！