请教prep数学题

boystar

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 the smallest prime factor of h(100) +1 , then  p is ？
答案：greater than 40

arthurman

94 = 2*47.  So 47 is a factor of h(100).

eeheaven

请问，这个47是怎么来的啊？

boystar

明白啦，谢谢楼上!

arthurman

This one has been explained before.

Basically,
1) These consecutive natural numbers h(100) and [h(100) + 1]  are co-prime, meaning that they do not share any prime numbers as their cofactors.  
2) h(100) contains all the prime numbers between 2 (from 2) and 47 (from 94).
3) Then prime numbers among factors of [h(100) + 1] would not include any prime numbers between 2 and 47.
4) Then the smallest prime facotr of [h(100) + 1] is bigger than 47.