pre数学救助

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

A  2<<10

B  10<<20

C  20<<30

D  30<<40

E  P>40

The answer is E

Puzzled, could any NN help to explain?  many thax

哦，知道怎么做了，发出来给不清楚的XDJM们分享哈

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

因为h(100)与h(100)+1是相邻的两个数，互质，没有共同的factors，而h(100)有从1到50的factors拉，所以h(100)+1就没有这个范围内的factors了哈，所以选E

应该是这样的，有NN来看请鉴定~~~