That sounds rather complicated! Surely there must be a more simple way of proving this?

- Jun 6th 2010, 11:49 AMyeah:)
- Jun 6th 2010, 12:03 PMgmatt
- Jun 6th 2010, 12:25 PMyeah:)
There must be an easier way! Has this forum given up?

- Jun 6th 2010, 01:57 PMhmmmm
i suggested an answers a few post ago, not sure if it is right though but nobody responded thanks to that strange interupption, hope it helps sorry for this messed up thread

- Jun 6th 2010, 02:20 PMgmatt
- Jun 6th 2010, 02:42 PMhmmmm
sorry if i am being stupid here but why does this mean that 10^(2^n) + 1 are excluded, surely they can be reduced using this same process?

- Jun 6th 2010, 02:46 PMchiph588@
- Jun 6th 2010, 03:32 PMyeah:)
So if the best mathematicians here are giving up, where do I go next?

- Jun 6th 2010, 03:41 PMchiph588@
- Jun 6th 2010, 04:12 PMtonio
- Jun 6th 2010, 04:27 PMyeah:)
If there is no solution, how can I show that there is no solution?

- Jun 6th 2010, 04:47 PMgmatt
You assume there exists a solution and show that it would imply a contradiction.

What you are asking is basically for a method to prove that a generalized fermat number (in this case $\displaystyle 10^{2^n}+1$ ) is not prime over a certain value of $\displaystyle n$ which is an open problem in mathematics as far as I know.

If this homework is from a computer-science class maybe your prof wants you to devise a method to test for primality, in which case Pepin's test would probably be the best approach (for deterministic primality, for probabilistic primality other algorithms may work better.)

Please refer to GFN10 factoring status if you don't believe me that this is an open problem. So far, up to $\displaystyle n=18$ Keller has compiled a list of known prime factors of the generalized fermat numbers, meaning they are all not prime.

You can read more about fermat numbers here

Generalized Fermat Number -- from Wolfram MathWorld

and here

Fermat number - Wikipedia, the free encyclopedia . - Jun 6th 2010, 05:13 PMyeah:)
Would anyone care to set out such an answer?

- Jun 6th 2010, 05:19 PMchiph588@
- Jun 6th 2010, 06:12 PMundefined
As gmatt said, this is an open problem in mathematics. Asking us to solve it for you is like asking us to prove or disprove the Goldbach conjecture or the Riemann hypothesis for you.

It may interest you to know that this exact question has been asked before on another thread in another forum (which I found through a Google search). Over there, someone came up with the spin of interpreting the numbers as given in base 2, for which the question can be easily answered. Except for that spin, the same conclusion was reached over there as over here.