求问pp上一道ps...

phoebedoll

For every positiveeven integer n, the function h(n) is defined to be the product of all the evenintegers from 2 to n, inclusive.  If p isthe smallest prime factor of h(100) + 1, then p is


(A) between 2 and10
(B) between 10 and20
(C) between 20 and30
(D) between 30 and40
(E) greater than 40

Rainbeauty

同问 帮着顶个 求NN answer

sdcar2010

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.