Determine the following number is prime or composite \[2^{2^{2011}+2011}+1\]

HINTS: There is a generalize form of this problem.

## Prime or Composite? With proof

### Prime or Composite? With proof

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### Re: Prime or Composite? With proof

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.### Re: Prime or Composite? With proof

hahaha. I am a grt fool. I dont check that, the power of 2 is odd. Thus the solution is so easy. By the way, the main problem is to prove $2^{2^k+s}+1$ is a composite number while $s \in \{1,2,3,4,...,(2^k-1)\}$.

**A man is not finished when he's defeated, he's finished when he quits.**

- Tahmid Hasan
**Posts:**665**Joined:**Thu Dec 09, 2010 5:34 pm**Location:**Khulna,Bangladesh.

### Re: Prime or Composite? With proof

actually i was the first one to prove it and sakal roy generalized it

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### Re: Prime or Composite? With proof

Let $s=2^lm$ with $m$ odd.Then we have $l<k$ and then $2^{2^k+s}+1=2^{2^l(2^{k-l}+m)}+1$ with $2^{k-l}+m$ odd

One one thing is neutral in the universe, that is $0$.