求问一道prep的数学

chenyuchen13

For every positive even integer n, thefunction h(n) is defined to be the product of all the even integers from 2 ton, 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


答案是E，智商有限，求解答！

justabeginning

2*4*6......*100=2^50*50!
因为相邻的两个数没有除一以外相同的因子，所以从2-50都不会是h(100)+1的因子，因此smallest prime 一定大于50，因此选E