求一道prep 数学题解答

summergal

For every positive even integer n, the function 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  

答案选E ，想不通，请大牛们帮忙解释一下

oeasy

shenchen

赞  32个

songxueer

h(100)+1=2*4*8*......*100+1=2^a*3^b*5^c*....*47+1
h(100)的质因数包含2到47之内的所有质数，所以h(100)+1不可能有低于47的质因数。