Smallest Prime Factor

[mullaneydan]

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 p is the smallest prime factor of h(100)+1, p is:

I forgot to write down all the choices, but the answer is >40. The answers all include ranges of numbers.

I thought to look for a pattern using a smaller (n). For instance,

n=4
(2x4)+1=9 3 is the SPF
n=6
(2x4x6)+1=49 7 is the SPF
n=8
(2x4x6x8)+1=385 5 is the SPF
n=10
(2x4x6x8x10)+1=3841 23 is the SPF


I know there must be a short cut or a way to look at this problem logically to make a quick assessment that the smallest prime factor is above 40.

[RonPurewal]

hi dan,

you should try using the search function before you post.
this is one of the most-often-posted problems on the entire forum, so you could've saved yourself a fair bit of time by searching for it.

here's one of the better threads on it:

post14808.html