Problem Solving

hello people...i faced this problem during my gmat pre 1 exam...i tried to solve it but jus cudnt... either i m missing a trick sumwhere or i m going wrong conceptually....plz help me out...thank you..

Q.3) For every positive integer n, function g (n) is given as product of all even integers from 2 to n, inclusive. If p is the smallest prime factor of g (100) + 1 then p could be :

1) Between 0 and 10
2) Between 10 and 20
.
.
.
Lets not waste time..the correct answer is (E) greater than 40.


Plz explain!!
Thanks in advance..