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## How to prove? Prime numbers. [closed]

$f(0)=4$

$f(x+1)=f(x)^2-2$

$\text{if} \quad 2^{x+2}-1|f(x) \quad \text{then} \quad 2^{x+2}-1 \quad \text{is prime}$

How to prove that?

Example:

$x=1$

$f(1)=14$,

$2^{1+2}-1=7$

and

$7|f(1) \implies 7$ is prime.

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See en.wikipedia.org/wiki/… . – Emil Jeřábek Nov 2 2011 at 15:50
This is (or is related to) Lehmer's congruence for Mersenne primes. You should be able to find online references which contain a proof sketch. Chris Caldwell's Prime Pages should have a proof or link to one; Hans Riesel's book on factoring should also have a proof. Gerhard "Ask Me About System Design" Paseman, 2011.11.02 – Gerhard Paseman Nov 2 2011 at 15:54
As pointed out on your Meta thread, you have been successfully asking questions on MSE. Your questions do appear to be undergraduate level. They will stay open longer on MSE, where there is no presumption that questions are current research. – Will Jagy Nov 2 2011 at 19:42