问道Prep的数学题，哪位大侠给讲一下

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 and 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

如题h(n)=2*4*6*8*...*n

h(100)+1=2*4*8*...*100+1=(1*2)*(2*2)*(3*2)*...*(50*2)+1=2^50*(1*2*3*...*50)+1

因此h(100)+1可以被任意1到50的整数除并余一，因此p>=50