# Composite number proof help

• Nov 5th 2007, 02:51 PM
katie07
Composite number proof help
Hello, I am having trouble with following proof:

Prove that all integers

2^2^(2n+1) +3 2^2^(4n+1) +7 , n = 1, 2, 3 ...

are composite.

Any help is appreciated , Thanks - Kate :)
• Nov 6th 2007, 03:51 AM
topsquark
Quote:

Originally Posted by katie07
Hello, I am having trouble with following proof:

Prove that all integers

2^2^(2n+1) +3 2^2^(4n+1) +7 , n = 1, 2, 3 ...

are composite.

Any help is appreciated , Thanks - Kate :)

I don't have time to do this in more detail, but my impression is that this might be doable by an induction proof.

-Dan

Edit: If it's going to be done by induction, it will take a better Mathematician than me!
• Nov 6th 2007, 10:26 AM
Jhevon
this is supposed to be $2^{2^{2n + 1}} + 3 \cdot 2^{2^{4n + 1}} + 7$ right?

i'm having trouble proving this is composite for n = 1, but i'm not that good with divisibility on such a large scale, the number is huge.