就解答PREP数学题

ubccoming

FOR every position even integer n,the function h(n) is defined to be the product of all even integers from 2 to n,inclusive. if p is the smallest prime factor of h(100)+1, then p is ?
A between 2 and 10
B between 10and 20
C between 20 and 30
D between 30 and 40
E greater than 40
答案是E,求解答！多谢

babybearmm

同问！

2^100*50!+1 最后两位肯定是01，可以推断出不被3、5、7整除，但是为什么是大于40咧……

avenue5th

h（100）+1=2*（1*2*3*....*500）+1 不能被任何50以下的数整除， 所有prime肯定大于50

coffeeqoo

h(100)+1=2^100*(1*2*3...*50) +1,其中最大的质数是47，所以加一后的最大质数必大于47，此题再本月 jj 有类似题目出现